Sufficient conditions for local regularity to the generalized Newtonian fluid with shear thinning viscosity

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• 作者：Hyeong-Ohk Bae ; Jörg Wolf
• 关键词：Weak solutions ; Local regularity ; Non ; Newtonian fluid ; Serrin ; type condition
• 刊名：Zeitschrift für angewandte Mathematik und Physik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：68
• 期：1
• 全文大小：
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1420-9039
• 卷排序：68

文摘

We prove the local regularity of a weak solution \({\varvec{u}}\) to the equations of a generalized Newtonian fluid with power law \(1< q \le 2\) if \({\varvec{u}}\) belongs to a suitable Lebesgue space. This result extends the well-known Serrin condition for weak solutions of the Navier–Stokes equations to the shear-thinning fluids.