Endpoint Strichartz estimates for the Klein–Gordon equation in two space dimensions and some applications |
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| Authors: | Jun Kato Tohru Ozawa |
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| Institution: | 1. Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan;2. Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA;3. Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan |
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| Abstract: | We prove the endpoint Strichartz estimates for the Klein–Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein–Gordon equation in two space dimensions for small data is also shown. |
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