论文标题
无粘性非线性BousSinesQ系统的几何结构的局部持久性
Local persistence of geometric structures of the inviscid nonlinear Boussinesq system
论文作者
论文摘要
受到最近发表的论文\ cite {hassainia-hmidi}的启发，目前的论文研究了常规$ 2d- $ boussinesq System的本地供应良好，以设置常规/单数涡流补丁。在初始涡度$ω_{0} = {\ bf 1} _ {d_0} $的条件下，带有$ \ poartial d_0 $的d_0 $是带有hölder规律性$ c^{1+\ ee}的jordan曲线我们还建立了段落贴片的局部规律性持久性。尽管在奇异斑块的情况下，由于系统的耦合现象和斑块的结构，分析非常复杂。为此，我们必须假设最初的非线性项是斑块边界奇异部分周围的恒定术语。
Inspired by the recently published paper \cite{Hassainia-Hmidi}, the current paper investigates the local well-posedness for the generalized $2d-$Boussinesq system in the setting of regular/singular vortex patch. Under the condition that the initial vorticity $ω_{0}={\bf 1}_{D_0}$, with $\partial D_0$ is a Jordan curve with a Hölder regularity $C^{1+\EE},\;0<\EE<1$ and the density is a smooth function, we show that the velocity vector field is locally well-posed and we also establish local-in-time regularity persistence of the advected patch. Although, in the case of the singular patch, the analysis is rather complicated due to the coupling phenomena of the system and the structure of the patch. For this purpose, we must assume that the initial nonlinear term is constant around the singular part of the patch boundary.
