Initial and boundary value problem of the unsteady Navier-Stokes system in the half-space with Hölder continuous boundary data

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• 作者：Tongkeun Chang^a ; ^{chang7357@yonsei.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Bum Ja Jin^b ; ^{bumjajin@hanmail.net" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Stokes ; Navier&ndash ; Stokes ; Nonhomogeneous boundary data ; Anisotropic Hö ; lder space ; Half-space
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1846-1869
• 全文大小：488 K

文摘

We study the initial–boundary value problem of the Navier–Stokes system in the half-space. We prove the unique solvability of the weak solution for some short time interval (0,T)$(0,T)$ with the velocity in $C^{\alpha ,\frac{\alpha }{2}}({\mathbb{R}}_{+}^n\times (0,T))$, cdde" title="Click to view the MathML source">0<α<1$0<\alpha <1$, when the given initial data in $C^{\alpha }({\mathbb{R}}_{+}^n)$ and the given boundary data in dd19185d9f8d9da258fdca">$C^{\alpha ,\frac{\alpha }{2}}({\mathbb{R}}^{n-1}\times (0,T))$ satisfy the compatibility conditions. Our result generalizes the result in [29] considering nonhomogeneous Dirichlet boundary data.