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

作　　者：Luhang Zhou Luhang Zhou(School of Mathematical Sciences, Chongqing Normal University, Chongqing, China)

机构地区：[1]School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第4期1286-1307,共22页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Local Well-Posedness ILL-POSEDNESS Gevrey Regularity 

分 类 号：O17[理学—数学]