2010 Fiscal Year Final Research Report
The Cauchy problem for the nonlinear wave equations of quantum mechanic
| Project/Area Number |
19740087
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Saitama University |
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Principal Investigator |
MACHIHARA Shuji Saitama University, 教育学部, 准教授 (20346373)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数方程式の大域理論 / 非線形現象 |
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| Research Abstract |
With Kimitoshi Tsutaya, we have obtained the time local well posedness for the nonlinear Dirac equation with some nonlocal nonlinear terms. Our result was critical in the sense of the scaling invariance for Sobolev norms. We first solved the problem in higher space dimensions, and later we solved the problem in 2 dimension.
With Kenji Nakanishi and Kotaro Tsugawa, we have obtained the time local and
global wellposedness for the Dirac-Klein-Gordon equation in 1 space dimension. We also have obtained illposedness for the same problem. This means we completely solved this problem.
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