修正Kawahara方程的收敛问题与色散爆破

Abstract

Abstract: This paper is concerned with the convergence problem and dispersive blow-up of the modified Kawahara equation. Firstly, by using the Fourier restriction norm method，high-low frequency tecnique and Strichartz estimates， this paper uses three different methods to prove that for almost everwhere x \in R, when t\longrightarrow0，　 u(x,t) converges to u_0(x) in H^{s}(\mathbb{R})(s\geq\frac{1}{4})， where u(x,t) is the solution and u_{0}(x) is the data. Secondly, by using Strichartz estimates and Fourier restriction norm method, this paper prove that when t\longrightarrow0, u(x,t) converges to U(t)u_0(x) uniformly with respect to $x$. Finally, this paper presents the dispersive blow-up.

Key words: Modified Kawahara equation, Pointwise convergence, Uniform convergence, Dispersive blow-up

CLC Number:

Wei-Min WANG Wei Yan. The convergence problem and dispersive blow-up of the modified Kawahara equation[J].Acta mathematica scientia,Series A, , (): 0-0.

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The convergence problem and dispersive blow-up of the modified Kawahara equation

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