论文标题
$ l^p $解决方案的全球存在和分析性，可压缩流体模型
Global existence and analyticity of $L^p$ solutions to the compressible fluid model of Korteweg type
论文作者
论文摘要
我们关注的是$ \ Mathbb {r}^{d}（d \ geq2）中的方程系统，该$可以用作相位过渡模型。对于零声速$ p'（ρ^{\ ast}）= 0 $，发现线性化系统允许\ textit {纯粹}抛物线结构，这使我们能够建立$ l^p $ -type $ l^p $ -type of l^p $ type of $ l^p $ type的全球及时存在和Gevrey强大解决方案的分析。确切地说，如果完整的粘度系数和毛细管系数满足$ \barν^2 \ geq4 \barκ$，则声波在可压缩的流体中不可用。因此，可以将先前的$ l^2 $限制在密度和速度的低频率上，可以将$ 1 \ leq p \ leq d $如果$ d \ geq2 $提高到一般的$ l^p $版本。证明主要依赖于新的非线性BESOV（-GEVREY）功能的组成。
We are concerned with a system of equations in $\mathbb{R}^{d}(d\geq2)$ governing the evolution of isothermal, viscous and compressible fluids of Korteweg type, that can be used as a phase transition model. In the case of zero sound speed $P'(ρ^{\ast})=0$, it is found that the linearized system admits the \textit{purely} parabolic structure, which enables us to establish the global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of $L^p$-type. Precisely, if the full viscosity coefficient and capillary coefficient satisfy $\barν^2\geq4\barκ$, then the acoustic waves are not available in compressible fluids. Consequently, the prior $L^2$ bounds on the low frequencies of density and velocity could be improved to the general $L^p$ version with $1\leq p\leq d$ if $d\geq2$. The proof mainly relies on new nonlinear Besov (-Gevrey) estimates for product and composition of functions.
