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Hs-global well-posedness for semilinear wave equations

✍ Scribed by Changxing Miao; Bo Zhang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
191 KB
Volume
283
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider the Cauchy problem for semilinear wave equations in R n with n 3. Making use of Bourgain's method in conjunction with the endpoint Strichartz estimates of Keel and Tao, we establish the H s -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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We prove that the Korteweg-de Vries initial-value problem is globally well-posed in H -3/4 (R) and the modified Kortewegde Vries initial-value problem is globally well-posed in H 1/4 (R). The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equat