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arXiv · 1905.12732

On a class of generalized solutions to equations describing incompressible viscous fluids

A. Abbatiello·E. Feireisl
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Abstract

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by the measure-valued solutions for the inviscid (Euler) system. We show the existence as well as the weak-strong uniqueness property in the class of dissipative solutions. Finally, the dissipative solution enjoying certain extra regularity coincides with a strong solution of the same problem.

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A. Abbatiello, E. Feireisl. 2019-05-29. On a class of generalized solutions to equations describing incompressible viscous fluids. https://arxiv.org/abs/1905.12732

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