Blowup criterion for the compressible fluid-particle interaction model in 3d with vacuum

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• 作者：Shijin DING^a ; ^{dingsj@scnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Bingyuan HUANG^b ; ^{huangby04@126.com" class="auth_mail" title="E-mail the corresponding author} ; Youbo LU^c ; ^{Lyb0813@m.scnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Blowup criterion ; compressible fluid-particle interaction model ; vacuum
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：36
• 期：4
• 页码：1030-1048
• 全文大小：306 K

文摘

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S025296021630056X&_mathId=si1.gif&_user=111111111&_pii=S025296021630056X&_rdoc=1&_issn=02529602&md5=74107197f9c1a6838f96451f0eea777c" title="Click to view the MathML source">L∞(0,T;L⁶)class="mathContainer hidden">class="mathCode">$L^{\infty }\left(0,T;L^6\right)$-norm of the density of particles and the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S025296021630056X&_mathId=si2.gif&_user=111111111&_pii=S025296021630056X&_rdoc=1&_issn=02529602&md5=4e334c4adac4bc76cbb9554f28dc7112" title="Click to view the MathML source">L1(0,T;L^∞)class="mathContainer hidden">class="mathCode">$L^1\left(0,T;L^{\mathrm{\infty }}\right)$-norm of the deformation tensor of velocity gradient.