2007 Fiscal Year Final Research Report Summary
Singular perturbation analysis of viscous fluid equations with Coriolis force term in the meteorological point of view
| Project/Area Number |
17540201
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido Information University |
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Principal Investigator |
MATSUI Shin'ya Hokkaido Information University, Faculty of media information science, Professor (50219367)
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| Co-Investigator(Kenkyū-buntansha) |
GIGA Yoshikazu The University of Tokyo, Graduate School of Mathematical Science, Professor
MAHALOV Alex Arizona State University, Department of Mathematics, Professor
SAAL Jurgen Hokkaido Information University, Department of Mathematics and Statistics, Doctor
INUI Katsuya Hokkaido Information University, Faculty of Science and Technology, Doctor
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| Project Period (FY) |
2005 – 2007
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| Keywords | The Navier-Stokes eauations / Fluid motion in a rotating filed / Singular parturbation / Metrological phenomena |
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| Research Abstract |
In this project, we analyzed existence and singular limit behavior of solutions for the Navier-Stokes equations with Coriolis force term in 3 dimensional whole space, 3 dimensional half space and Poincare domain :
1. We discussed the Cauchy problem for the 3dimensional Navier-Stokes equations with Coriolis force term. Here, for initial data we employed a vector of a class of solenoidal bounded vector fields. In this case the existence time of solution is depends on the Coriolis force parameter (a half of angular velocity speed around rotating axis). (Joint work with Giga, Inui and Mahalov)
2. If initial date for the Cauchy problem of our problem is a Fourier inversed image of Radon measure whose support does not include the origin, the existence time of a solution is NOT independent of Coriolis parameter. (Joint work with Giga, Inui and Mahalov)
3. We considered initial boundary problem in 3 dimensional half space. The solution of our problem is constructed around the Eckman boundary layer solution, whose tangential component is not required to be zero and whose normal component is close to be Eckman boundary layer solution at normal space component infinity in the norm of L^p. ((Joint work with Giga, Inui, Mahalov and Saal))
4. The stationary solutions of our problem in 3 dimensional Poincare domain are not almost be unique in L^2 space. If Coriolis force parameter goes to infinity, all stationary solution is close to the state which is independ of the direction of rotating axis. This singular perturbation is in H^2 (strong convergence). Furthermore if our domain is simple, stationary solutions convergence to the mean with respect to rotating axis of a singular perturbation limit. (Joint work with Inui and Mahalov)
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Research Products
(12 results)
