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 fo...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.展开更多
文摘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.
