Strichartz estimates for dispersive equations and solvability of the Kawahara equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:304

Article

Cui, SB ; Tao, SP

关键词: Strichartz estimate;    dispersive equation;    Kawahara equation;    global existence;   

DOI  :  10.1016/j.jmaa.2004.09.049

来源: Elsevier

【 摘 要 】

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 partial derivative(t)u + au partial derivative(x)u +beta partial derivative(3)(x)u + gamma partial derivative(5)(x)u = 0 in the class C(R, H-s(R)). Local existence is proved for s > 1/4 and global existence is proved for s >= 2. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free