On Liouville type theorems for the steady Navier-Stokes equations in

详细信息    查看全文

• 作者：Dongho Chae^a ; ^{dchae@cau.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Jö ; rg Wolf^b ; ^{jwolf@math.hu-berlin.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q30 ; 76D05
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5541-5560
• 全文大小：283 K

文摘

In this paper we prove three different Liouville type theorems for the steady Navier–Stokes equations in R³${\mathbb{R}}^3$. In the first theorem we improve logarithmically the well-known $L^{\frac{9}{2}}({\mathbb{R}}^3)$ result. In the second theorem we present a sufficient condition for the trivially of the solution (v=0$v=0$) in terms of the head pressure, $Q=\frac{1}{2}|v{|}^2+p$. The imposed integrability condition here has the same scaling property as the Dirichlet integral. In the last theorem we present Fubini type condition, which guarantee v=0$v=0$.