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

0524629 - MÚ 2021 RIV DE eng J - Journal Article
Abbatiello, A. - Feireisl, Eduard
On a class of generalized solutions to equations describing incompressible viscous fluids.
Annali di Matematica Pura ed Applicata. Roč. 199, č. 3 (2020), s. 1183-1195. ISSN 0373-3114. E-ISSN 1618-1891
Institutional support: RVO:67985840
Keywords : generalized viscous fluid * weak solution * weak–strong uniqueness
OECD category: Pure mathematics
Impact factor: 0.969, year: 2020
Method of publishing: Open access
https://doi.org/10.1007/s10231-019-00917-x

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.
Permanent Link: http://hdl.handle.net/11104/0308966