Well-posedness and stability of incompressible and compressible flows with phase transition

• Project/Area Number: 16H03945
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Kyoto University
• Principal Investigator: Shimizu Senjo 京都大学, 人間・環境学研究科, 教授 (50273165)
• Co-Investigator(Kenkyū-buntansha): 森本 芳則 京都大学, 人間・環境学研究科, 名誉教授 (30115646) ; 小林 孝行 大阪大学, 基礎工学研究科, 教授 (50272133)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000); Fiscal Year 2020: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2019: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2016: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
• Keywords: 偏微分方程式 / Navier-Stokes方程式 / 最大正則性 / 自由境界問題 / 関数解析 / 調和解析 / 実解析 / 微分幾何 / 時間大域的適切性 / 初期値問題 / 初期値-境界値問題 / 流体方程式 / 函数方程式論 / 解析学 / 数理解析 / 圧縮性粘性流体 / 相転移 / 2相流体 / 局所適切性 / 関数方程式論 / 関数解析学

Outline of Final Research Achievements

The following results were obtained in this study. 1) Stability of free boundary problems for incompressible two-phase fluids incorporating thermodynamic equilibrium, 2) Maximal L1-regularity theorem for inhomogeneous boundary data, 3) Time global solution of Navier-Stokes equations in unbounded domains for non-decaying initial data, 4) Stability of solutions of the electromagnetic fluid equations based on maximal regularity, 5) Regularity and stability of the Navier-Stokes equations in scale-invariant spaces based on maximal regularity, and 6) Helmholtz--Weyl type decomposition theorem for Lr-vector fields.

Academic Significance and Societal Importance of the Research Achievements

空気や水などの流体の動きはNavier-Stokes方程式という非線形な偏微分方程式によって記述される. 天気予報や海底探索、飛行機の設計や橋の建設などの基礎となるこの方程式に対して, 与えられた初期条件や外力に対して解が時間大域的に存在するか、一意的であるか、滑らかさはどの程度か、安定であるかについて関数解析や調和解析、実解析に基づき数学的に厳密な立場から解析するものである.

Research Products

• [Int'l Joint Research] Darmstadt工科大学/Karlsruhe工科大学(ドイツ)
• [Int'l Joint Research] ダルムシュタッド工科大学(ドイツ)
• [Int'l Joint Research] TU Darmstadt(ドイツ)
• [Int'l Joint Research] U. Campania(イタリア)
• [Int'l Joint Research] Martin-Luther University(ドイツ)
• [Int'l Joint Research] University of Campania Luigi Vanvitelli(イタリア)
• [Int'l Joint Research] Martin Luther University of Halle(ドイツ)
• [Int'l Joint Research] The University of Naples Federico II(イタリア)
• [Journal Article] Analyticity in space-time of solutions to the Navier-Stokes equations via parameter trick based on maximal regularity (2023)
  • Author(s): H. Kozono, P. Kunstmann, S. Shimizu
  • Journal Title: Annali di Scienze Scuola Normale Superiore Volume: to appear Pages: 1673-1716
  • DOI: 10.2422/2036-2145.202109_011
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Stability of stationary solutions to the Navier-Stokes equations in the Besov space (2023)
  • Author(s): H. Kozono, S. Shimizu
  • Journal Title: Math. Nachr. Volume: to appear Issue: 5 Pages: 1964-1982
  • DOI: 10.1002/mana.202100150
  • Peer Reviewed
• [Journal Article] 3次元L^rベクトル場に対するHelmholtz-Weyl分解 (2023)
  • Author(s): 小薗英雄, 清水扇丈, 柳沢卓
  • Journal Title: 数学（日本数学会編集, 岩波書店発売） Volume: 75 (1)
  • Peer Reviewed
• [Journal Article] A Characterization of harmonic Lr-vector fields in three dimensional exterior domains (2022)
  • Author(s): M. Hieber, H. Kozono, A. Seyfert, S. Shimizu, T. Yanagisawa
  • Journal Title: J. Geom. Anal. Volume: 32 Issue: 7
  • DOI: 10.1007/s12220-022-00938-8
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Maximal L^1-regularity for parabolic initial-boundary value problems with inhomogeneous data (2022)
  • Author(s): Ogawa Takayoshi、Shimizu Senjo
  • Journal Title: Journal of Evolution Equations Volume: 22 Issue: 2
  • DOI: 10.1007/s00028-022-00778-7
  • Peer Reviewed / Open Access
• [Journal Article] Maximal regularity for the Cauchy problem of the heat equation?in <i>BMO</i> (2022)
  • Author(s): Ogawa Takayoshi、Shimizu Senjo
  • Journal Title: Mathematische Nachrichten Volume: 295 Issue: 7 Pages: 1406-1442
  • DOI: 10.1002/mana.201900506
  • Peer Reviewed / Open Access
• [Journal Article] Global well-posedness for incompressible Navier-Stokes equations in the critical Besov spaces under the Lagrangian coordinate (2021)
  • Author(s): T. Ogawa, S. Shimizu
  • Journal Title: J. Differential Equations Volume: 274 Pages: 613-651
  • DOI: 10.1016/j.jde.2020.10.023
  • Peer Reviewed
• [Journal Article] The Helmholtz-Weyl decomposition of Lr vector fields for two dimensional exterior domains (2021)
  • Author(s): M.Hieber, H.Kozono, A.Seyfert, S.Shimizu, T.Yanagisawa
  • Journal Title: J. Geom. Anal. Volume: 31 Issue: 5 Pages: 5146-5165
  • DOI: 10.1007/s12220-020-00473-4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Maximal L1-regularity for parabolic boundary value problems with inhomogeneous data in the half-space (2020)
  • Author(s): T. Ogawa, S. Shimizu
  • Journal Title: Proc. Japan Acad. Volume: 96 Issue: 7 Pages: 57-62
  • DOI: 10.3792/pjaa.96.011
  • Peer Reviewed
• [Journal Article] Global existence and time decay estimate of solutions to the compressible Navier?Stokes?Korteweg system under critical condition (2020)
  • Author(s): Kobayashi Takayuki、Tsuda Kazuyuki
  • Journal Title: Asymptotic Analysis Volume: To appear Issue: 2 Pages: 1-23
  • DOI: 10.3233/asy-201600
  • Peer Reviewed / Open Access
• [Journal Article] Characterization of initial data in the homgeneous Besov space for solutions in the Serrin class of the Navier-Stokes equations (2020)
  • Author(s): H. Kozono, A. Okada, S. Shimizu
  • Journal Title: J. Funct. Anal. Volume: 278 Issue: 5 Pages: 108390-108390
  • DOI: 10.1016/j.jfa.2019.108390
  • NAID: 120006888266
  • Peer Reviewed
• [Journal Article] Global existence of weak solutions to 3D Navier-Stokes IBVP with non-decaying initial data in exterior domains (2020)
  • Author(s): P. Maremonti, S. Shimizu
  • Journal Title: J. Differential Equations Volume: 269 Issue: 2 Pages: 1612-1635
  • DOI: 10.1016/j.jde.2020.01.021
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A Characterization of Harmonic Lr-Vector Fields in Two-Dimensional Exterior Domains (2020)
  • Author(s): M. Hieber, H. Kozono, A. Seyfert, S. Shimizu, T. Yanagisawa
  • Journal Title: The Journal of Geometric Analysis Volume: Online Issue: 4 Pages: 3742-3759
  • DOI: 10.1007/s12220-019-00216-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Strong solutions of the Navier-Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces (2019)
  • Author(s): H. Kozono, S. Shimizu
  • Journal Title: J. Funct. Anal. Volume: 276 Issue: 3 Pages: 896-931
  • DOI: 10.1016/j.jfa.2018.06.006
  • Peer Reviewed
• [Journal Article] Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity (2019)
  • Author(s): K. Kaneko, H. Kozono, S. Shimizu
  • Journal Title: Indiana U. Math. J. Volume: 68 Issue: 3 Pages: 857-880
  • DOI: 10.1512/iumj.2019.68.7650
  • Peer Reviewed
• [Journal Article] Global well-posedness and time-decay estimates of the compressible Navier-Stokes-Korteweg system in critical Besov spaces (2019)
  • Author(s): Noboru Chikami and Takayuki Kobayashi
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 印刷中 Issue: 2 Pages: 1-32
  • DOI: 10.1007/s00021-019-0431-8
  • Peer Reviewed / Open Access
• [Journal Article] Time-space L2-boundedness for the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equations (2019)
  • Author(s): T. Kobayashi , M. Misawa and K. Nakamura
  • Journal Title: Tsukuba J. Mathematics Volume: 43
  • Peer Reviewed
• [Journal Article] Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane (2018)
  • Author(s): Paolo Maremonti, Senjo Shimizu
  • Journal Title: J. Differential Equations Volume: 265 Issue: 10 Pages: 5352-5383
  • DOI: 10.1016/j.jde.2018.07.004
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Navier-Stokes equations with external forces in time-weighted Besov spaces. (2018)
  • Author(s): Kozono, H., Shimizu, S.
  • Journal Title: Math. Nach. Volume: 291 Issue: 11-12 Pages: 1781-1800
  • DOI: 10.1002/mana.201700078
  • Peer Reviewed
• [Journal Article] Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in exterior domains (2018)
  • Author(s): Paolo Maremonti, Senjo Shimizu
  • Journal Title: J. Math. Fluid Mech. Volume: 20 Issue: 3 Pages: 899-927
  • DOI: 10.1007/s00021-017-0348-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On a Navier-Stokes-Ohm problem from plasma physics (2018)
  • Author(s): Jan Pruess, Senjo Shimizu
  • Journal Title: J. Evol. Equ. Volume: 18 Issue: 2 Pages: 351-371
  • DOI: 10.1007/s00028-017-0404-4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Strong solutions of the Navier-Stokes equations with singular data. Mathematical analysis in fluid mechanics (2018)
  • Author(s): Hideo Kozono, Senjo Shimizu
  • Journal Title: Contemp. Math., Amer. Math. Soc., Providence Volume: 710 Pages: 163-173
  • DOI: 10.1090/conm/710/14369
  • Peer Reviewed
• [Journal Article] Navier-Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions. (2018)
  • Author(s): Kozono, H., Shimizu, S.
  • Journal Title: J. Math. Anal. Appl. Volume: 458 Issue: 2 Pages: 1693-1708
  • DOI: 10.1016/j.jmaa.2017.10.048
  • Peer Reviewed
• [Journal Article] Remark on the uniqueness of a mild solution of the Boltzmann equation in the critical Besov space (2017)
  • Author(s): Takayoshi Ogawa, Senjo Shimizu
  • Journal Title: RIMS Kokuroku Bessatsu Volume: B67 Pages: 83-105
  • Peer Reviewed
• [Journal Article] Qualitative behaviour of incompressible two-phase flows with phase transitions: the isothermal case (2017)
  • Author(s): Jan Pruess, Senjo Shimizu
  • Journal Title: Proc. Indian Acad. Sci. Math. Sci. Volume: 127 Issue: 5 Pages: 815-831
  • DOI: 10.1007/s12044-017-0365-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On local Lp-Lq well-posedness of incompressible two-phase flows with phase transitions: Non-equal densities with large initial data (2017)
  • Author(s): S. Shimizu, S. Yagi
  • Journal Title: Advances in Differential Equations Volume: -
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Modeling of two-phase flows with and without phase transitions (2016)
  • Author(s): J. Pruss, S. Shimizu
  • Journal Title: Handbook of Mathematical Analysis in Mechanics of Viscous Fluid Volume: - Pages: 1-38
  • DOI: 10.1007/978-3-319-10151-4_24-1
  • ISBN: 9783319101514
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On Incompressible two-phase flows with phase transition and variable surface tension (2016)
  • Author(s): Jan Pruess, Senjo Shimizu, Gieri Simonett, Mathias Wilke
  • Journal Title: Recent Developments of Mathematical Fluid Mechanics Volume: -- Pages: 411-442
  • DOI: 10.1007/978-3-0348-0939-9_22
  • ISBN: 9783034809382, 9783034809399
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Global solutions in the critical Besov space for the non-cutoff Boltzmann equation (2016)
  • Author(s): Y. Morimoto, S. Sakamoto
  • Journal Title: J. Differential Equations Volume: 261 Issue: 7 Pages: 4073-4134
  • DOI: 10.1016/j.jde.2016.06.017
  • Peer Reviewed
• [Journal Article] Measure valued solutions to the spatially homogeneous Boltzmann equation without angular cutoff (2016)
  • Author(s): Y. Morimoto, S. Wang, T. Yang
  • Journal Title: J. Stat. Phys. Volume: 165 Issue: 5 Pages: 866-906
  • DOI: 10.1007/s10955-016-1655-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Weighted Lp － Lq Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations (2016)
  • Author(s): T. Kobayashi and T. Kubo
  • Journal Title: Recent Developments of Mathematical Fluid Mechanics, Advances in Mathematical Fluid Mechanics Volume: なし Pages: 337-349
  • DOI: 10.1007/978-3-0348-0939-9_18
  • ISBN: 9783034809382, 9783034809399
  • Peer Reviewed / Open Access
• [Presentation] Free boundary problems for the incompressible Navier-Stokes equations in critical spaces (2022)
  • Author(s): Senjo Shimizu
  • Organizer: Mathematical Advances in Geophysical Fluid Dynamics (2246) Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Int'l Joint Research / Invited
• [Presentation] Free boundary problems for the incompressible Navier-Stokes equations in critical spaces (2022)
  • Author(s): 清水扇丈
  • Organizer: 広島微分方程式研究集会, 広島大学
  • Invited
• [Presentation] Free boundary problems for the incompressible Navier-Stokes equations in critical spaces (2022)
  • Author(s): Senjo Shimizu
  • Organizer: Nonlinear PDEs in Fluid Dynamics, CIRM, France
  • Int'l Joint Research / Invited
• [Presentation] On the compressible Navier-Stokes-Korteweg system under the critical condition (2022)
  • Author(s): 小林孝行
  • Organizer: Dispersive and wave equations, 大阪大学
  • Invited
• [Presentation] 圧縮性 Navier-Stokes-Korteweg 方程式の大域的適切性について (2022)
  • Author(s): 小林孝行
  • Organizer: 研究集会「非線型偏微分方程式と走化性」, 北九州国際会議場
  • Invited
• [Presentation] Global well-posedness of the compressible Navier-Stokes-Korteweg system under critical condition (2022)
  • Author(s): Takayuki Kobayashi
  • Organizer: International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics, 早稲田大学
  • Int'l Joint Research / Invited
• [Presentation] 圧縮性 Navier-Stokes-Korteweg 方程式の時間大域解の存在と解の漸近挙動について (2022)
  • Author(s): 小林孝行
  • Organizer: 第10回弘前非線形方程式研究会, 弘前大学
  • Invited
• [Presentation] Resolvent problems for a compressible fluid model of Korteweg type in bounded domains (2022)
  • Author(s): 小林孝行
  • Organizer: 北九州における偏微分方程式研究集会, 北九州国際会議場
  • Invited
• [Presentation] Maximal L1-regularity and a free boundary problem for the incompressible Navier-Stokes equations (2021)
  • Author(s): Senjo Shimizu
  • Organizer: Lecture series on Mathematical Fluid Dynamics in Waseda, "Maximal Regularity Theorem and Mathematical Fluid Dynamics"
  • Int'l Joint Research / Invited
• [Presentation] Maximal L1-regularity and a free boundary problem for the incompressible Navier-Stokes equations (2020)
  • Author(s): Senjo Shimizu
  • Organizer: Vorticity, Rotation and Symmetry (V) Global Results and Nonlocal Phenomena, CIRM (Hybrid)
  • Int'l Joint Research / Invited
• [Presentation] 半空間放物型方程式の初期値境界値問題に対する最大L1正則性 (2020)
  • Author(s): 清水扇丈
  • Organizer: 東京理科大学理工学部数学科談話会
  • Invited
• [Presentation] Maximal L1-regularity for parabolic boundary value problems with inhomogeneous data in the half-space (2020)
  • Author(s): Senjo Shimizu
  • Organizer: The Eighth Pacific RIM Conference in Mathematics, Berkeley (Online)
  • Int'l Joint Research / Invited
• [Presentation] 非斉次境界条件を持つ半空間放物型方程式の初期値境界値問題に対する最大L^1正則性 (2020)
  • Author(s): 清水扇丈
  • Organizer: Critical exponent and nonlinear evolution equations 2020, 東京理科大学神楽坂キャンパス, 2020年2月14日
  • Invited
• [Presentation] 半空間での放物型方程式の初期値境界値問題に対する最大L^1正則性 (2020)
  • Author(s): 小川卓克, 清水扇丈
  • Organizer: 日本数学会年会 函数方程式論分科会, 日本大学, 2020年3月19日
• [Presentation] Maximal L^1-regularity for the parabolic boundary value problem with inhomogeneous data in the half-space (2019)
  • Author(s): Senjo Shimizu
  • Organizer: Evolution Equations: Abstract and Applied Perspectives in Honour of the 60th Birthday of Matthias Hieber, Luminy, CIRM, France, October 28th-November 1st, 2019
  • Int'l Joint Research / Invited
• [Presentation] 半空間放物型方程式の初期値境界値問題に対する最大L^1正則性 (2019)
  • Author(s): 清水扇丈
  • Organizer: 東北大学応用数理解析セミナー, 東北大学大学院理学研究科, 2019年12月13日
  • Invited
• [Presentation] Characterization of initial data in the homgeneous Besov space for solutions in the Serrin class of the Navier-Stokes equations (2019)
  • Author(s): 清水扇丈
  • Organizer: 第16回浜松偏微分方程式研究集会（静岡大学浜松キャンパス）
  • Invited
• [Presentation] Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane (2019)
  • Author(s): Paolo Maremonti, 清水扇丈
  • Organizer: 2019年度日本数学会年会（東京工業大学）, 函数方程式論分科会
• [Presentation] On stability of a Navier-Stokes-Ohm problem from plasma physics (2019)
  • Author(s): Jan Pruess, 清水扇丈
  • Organizer: 2019年度日本数学会年会（東京工業大学）, 函数方程式論分科会
• [Presentation] 斉次Besov空間に初期値をとるNavier-Stokes方程式の解の一意存在とその解析性 (2018)
  • Author(s): 岡田晃, 小薗英雄, 清水扇丈
  • Organizer: 2018年度日本数学会年会（東京大学）, 函数方程式論分科会
• [Presentation] Necessary and sufficient condition on initial data for solutions in the Serrin class of the Navier-Stokes equations (2018)
  • Author(s): Senjo Shimizu
  • Organizer: Mathematical Fluid Mechanics and Related Topics（東京工業大学）
  • Int'l Joint Research / Invited
• [Presentation] Characterization of initial data in the homogeneous Best space for solutions in the Serrin class of the Navier-Stokes equations (2018)
  • Author(s): Senjo Shimizu
  • Organizer: International Conference on PDEs from Fluids, Wuhan University, Wuhan, China
  • Int'l Joint Research / Invited
• [Presentation] Characterization of initial data in the homogeneous Best space for solutions in the Serrin class of the Navier-Stokes equations (2018)
  • Author(s): 清水扇丈
  • Organizer: RIMS共同研究（公開型）「関数空間の一般化とその周辺」
  • Invited
• [Presentation] Characterization of initial data in the homgeneous Besov space for solutions in the Serrin class of the Navier-Stokes equations (2018)
  • Author(s): 清水扇丈
  • Organizer: 第８回弘前非線形方程式研究会（弘前大学）
  • Invited
• [Presentation] Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in exterior domains (2017)
  • Author(s): P. Maremonti, 清水扇丈
  • Organizer: 日本数学会年会函数方程式論分科会一般講演
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-27
• [Presentation] Besov空間値の最大Lorentz正則性に基づくNavier-Stokes方程式の強解について (2017)
  • Author(s): 小薗英雄, 清水扇丈
  • Organizer: 日本数学会年会函数方程式論分科会一般講演
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-27
• [Presentation] Strong solutions of the Navier-Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces (2017)
  • Author(s): Senjo Shimizu
  • Organizer: Vorticity, Rotation and Symmetry (IV); Complex Fluids and the Issue of Regularity, CIRM, France.
  • Int'l Joint Research / Invited
• [Presentation] Strong solutions of the Navier-Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces (2017)
  • Author(s): Senjo Shimizu
  • Organizer: The 13th KWMS International Conference, POSTECH, Korea.
  • Int'l Joint Research / Invited
• [Presentation] Besov空間値の最大Lorentz正則性に基づくNavier-Stokes方程式の強解について (2017)
  • Author(s): 清水扇丈
  • Organizer: 第6回岐阜数理科学研究集会（岐阜大学サテライトキャンパス）
  • Invited
• [Presentation] Navier-Stokes方程式の強解の正則性と漸近挙動 (2017)
  • Author(s): 岡田晃, 小薗英雄, 清水扇丈
  • Organizer: 2017年度日本数学会秋季総合分科会（山形大学）, 函数方程式論分科会
• [Presentation] 定温条件下での相転移を伴う2相流体について (2016)
  • Author(s): 清水扇丈
  • Organizer: 京都大学大学院理学研究科/数理解析研究所談話会
  • Place of Presentation: 京都大学（京都府、京都市）
  • Year and Date: 2016-10-05
  • Int'l Joint Research
• [Presentation] Two-phase flows with phase transitions (2016)
  • Author(s): J. Pruss, S. Shimizu
  • Organizer: The Asian Mathematical Conference 2016
  • Place of Presentation: Bali (Indonesia)
  • Year and Date: 2016-07-25
  • Int'l Joint Research / Invited
• [Presentation] Two-phase flows with phase transitions (2016)
  • Author(s): J. Pruss, S. Shimizu
  • Organizer: International Conference on Navier-Stokes Equations and Related PDE's
  • Place of Presentation: Daejeon (Korea)
  • Year and Date: 2016-06-23
  • Int'l Joint Research / Invited
• [Presentation] Two-phase flows with phase transitions (2016)
  • Author(s): J. Pruss, S. Shimizu
  • Organizer: International Conference on Evolution Equations
  • Place of Presentation: Nashville (USA)
  • Year and Date: 2016-05-16
  • Int'l Joint Research / Invited
• [Presentation] Local existence of isothermal compressible two-phase flows with phase transitions (2016)
  • Author(s): 清水扇丈
  • Organizer: 第29回「南大阪応用数学セミナー」
  • Place of Presentation: 大阪府立大学（大阪府、堺市）
  • Year and Date: 2016-04-16
• [Funded Workshop] Maximal regularity and nonlinear PDE (RIMS共同研究（公開型）特別計画） (2019)
• [Funded Workshop] Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics (2016)
  • Place of Presentation: 京都大学百周年百周年時計台記念館（京都府、京都市）
  • Year and Date: 2016-05-27