JournalsaihpcVol. 31, No. 2pp. 267–279

On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation

  • Jingjing Liu

    Department of Mathematics and Information Science, Zhengzhou University of Light Industry, 450002 Zhengzhou, China

  • Zhaoyang Yin

    Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China
On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation cover
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Abstract

In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.

Cite this article

Jingjing Liu, Zhaoyang Yin, On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, pp. 267–279

DOI 10.1016/J.ANIHPC.2013.02.008