H-global well-posedness for semilinear wave equations |
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| Authors: | Changxing Miao |
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| Affiliation: | a Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China
b School of Mathematical and Information Sciences, Coventry University, Coventry CV1 5FB, UK |
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| Abstract: | We consider the Cauchy problem for semilinear wave equations in  with n?3. Making use of Bourgain's method in conjunction with the endpoint Strichartz estimates of Keel and Tao, we establish the Hs-global well-posedness with s<1 of the Cauchy problem for the semilinear wave equation. In doing so a number of nonlinear a priori estimates is established in the framework of Besov spaces. Our method can be easily applied to the case with n=3 to recover the result of Kenig-Ponce-Vega. |
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| Keywords: | Wave equations Strichartz estimates Besov spaces Well-posedness |
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