2010 Fiscal Year Final Research Report
Local smoothing estimates for hyperbolic and dispersive equations and applications
| Project/Area Number |
20540165
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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 |
Basic analysis
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| Research Institution | Mie University |
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Principal Investigator |
HIDANO Kunio Mie University, 教育学部, 准教授 (00285090)
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| Project Period (FY) |
2008 – 2010
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| Keywords | Strichartz型評価式 / 波動方程式 / 局所平滑化評価式 |
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| Research Abstract |
Abstract Strichartz estimates have been obtained for wave equations outside obstacles. As an application, the global (in time) existence of small solutions to semilinear wave equations with power-type nonlinear terms has been proved in 3-D domain outside obstacles.
Weighted space-time L^2 estimates have been also obtained for wave equations with space-time dependent variable coefficients. As an application, some new results on local (in time) wellposedness have been proved for quasilinear wave equations with low regularity radial data.
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