On Liouville type theorems for the steady Navier-Stokes equations in
详细信息 查看全文
- 作者：Dongho Chae<sup>asup><sup> ; sup><sup>dchae@cau.ac.kr" class="auth_mail" title="E-mail the corresponding authorsup> ; Jö ; rg Wolf<sup>bsup><sup> ; sup><sup>jwolf@math.hu-berlin.de" class="auth_mail" title="E-mail the corresponding authorsup>
- 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 <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302194&_mathId=si1.gif&_user=111111111&_pii=S0022039616302194&_rdoc=1&_issn=00220396&md5=69a54831ff1daf12cb981ef6aa1f53f0" title="Click to view the MathML source">R<sup>3sup>span><span class="mathContainer hidden"><span class="mathCode">span>span>span>. In the first theorem we improve logarithmically the well-known <span id="mmlsi2" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302194&_mathId=si2.gif&_user=111111111&_pii=S0022039616302194&_rdoc=1&_issn=00220396&md5=62358d6aa384b8c236d18e186eb0d91a">![]()
ss="imgLazyJSB inlineImage" height="21" width="51" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022039616302194-si2.gif">script>![]()
style="vertical-align:bottom" width="51" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022039616302194-si2.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> result. In the second theorem we present a sufficient condition for the trivially of the solution (<span id="mmlsi28" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302194&_mathId=si28.gif&_user=111111111&_pii=S0022039616302194&_rdoc=1&_issn=00220396&md5=f91db8c2fe7631618ddb1d9e2aa1e1a5" title="Click to view the MathML source">v=0span><span class="mathContainer hidden"><span class="mathCode">span>span>span>) in terms of the head pressure, <span id="mmlsi4" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302194&_mathId=si4.gif&_user=111111111&_pii=S0022039616302194&_rdoc=1&_issn=00220396&md5=91b699a75f0e3e3c37ab4406ec9b2a5e">![]()
ss="imgLazyJSB inlineImage" height="22" width="96" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022039616302194-si4.gif">script>![]()
style="vertical-align:bottom" width="96" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022039616302194-si4.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>. 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 <span id="mmlsi28" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302194&_mathId=si28.gif&_user=111111111&_pii=S0022039616302194&_rdoc=1&_issn=00220396&md5=f91db8c2fe7631618ddb1d9e2aa1e1a5" title="Click to view the MathML source">v=0span><span class="mathContainer hidden"><span class="mathCode">span>span>span>.