Fujita-Kato theorem for the 3-D inhomogeneous Navier-Stokes equations

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• 作者：Dongxiang Chen^a ; ^{chendx020@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Zhifei Zhang^b ; ^{zfzhang@math.pku.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Weiren Zhao^c ; ^{zjzjzwr@126.com" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 July 2016
• 年：2016
• 卷：261
• 期：1
• 页码：738-761
• 全文大小：320 K

文摘

In this paper, we prove the global existence and uniqueness of the solution with discontinuous density for the 3-D inhomogeneous Navier–Stokes equations if the initial data (ρ₀,u₀)∈L^∞(R³)×H^s(R³)$({\rho }_0,u_0)\in L^{\infty }({\mathbb{R}}^3)\times H^s({\mathbb{R}}^3)$ with $s>\frac{1}{2}$ satisfies for some small ε>0$\epsilon >0$ depending only on c₀$c_0$, C₀$C_0$. Furthermore, we introduce the dual method to show that if u₀∈L^p(R³)$u_0\in L^p({\mathbb{R}}^3)$ for $p\in [\frac{6}{5},2]$, the velocity satisfies the decay estimate with .