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.