A remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions

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• 作者：Hideo Kozono^a ; ^{kozono@waseda.jp" class="auth_mail" title="E-mail the corresponding author} ; Yutaka Terasawa^b ; ^{yutaka@math.nagoya-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yuta Wakasugi^b ; ^{yuta.wakasugi@math.nagoya-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q30 ; 35B53 ; 76D05
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：272
• 期：2
• 页码：804-818
• 全文大小：327 K

文摘

Consider the 3D homogeneous stationary Navier–Stokes equations in the whole space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616301562&_mathId=si1.gif&_user=111111111&_pii=S0022123616301562&_rdoc=1&_issn=00221236&md5=f67a3e7303b657c5a234b2e17ff9efab" title="Click to view the MathML source">R³class="mathContainer hidden">class="mathCode">${\mathbb{R}}^3$. We deal with solutions vanishing at infinity in the class of the finite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance.