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https://doi.org/10.3934/dcds.2014.34.843

has been cited by the following article:

• TITLE: On the Cauchy Problem for Mildly Nonlinear and Non-Boussinesq Case-(ABC) System

  AUTHORS: Luhang Zhou

  KEYWORDS: Local Well-Posedness, Ill-Posedness, Gevrey Regularity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.4, April 29, 2024

  ABSTRACT: In this paper, we investigate the local well-posedness, ill-posedness, and Gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution for this system in Besov spaces B p,r s 1 × B p,r s with 1≤p,r≤∞ and s>max{ 1 1 p , 3 2 } was firstly established. Next, we consider the continuity of the solution-to-data map, i.e. the ill-posedness of the solution for this system in Besov space B p,∞ s 1 × B p,∞ s was derived. Finally, the Gevrey regularity of the system was presented.