Acta mathematica scientia,Series A

   

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

Wei-Min WANG,Wei Yan   

  1. Henan Normal University
  • Received:2023-08-16 Revised:2024-01-02 Published:2024-01-26
  • Contact: Wei-Min WANG

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: 

  • O1
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