Strichartz estimates for dispersive equations and solvability of the Kawahara equation |
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| Authors: | Shangbin Cui Shuangpin Tao |
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| Institution: | a Institute of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, People's Republic of China
b Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, People's Republic of China |
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| Abstract: | We first establish a series of Strichartz estimates for a general class of linear dispersive equations by applying the theory of oscillatory integrals established by Kenig, Ponce and Vega. Next we use such estimates to study solvability of the Cauchy problem of the Kawahara equation  in the class C(R,Hs(R)). Local existence is proved for s>1/4 and global existence is proved for s?2. |
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| Keywords: | Strichartz estimate Dispersive equation Kawahara equation Global existence |
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