Generalized solutions to models of compressible viscous fluids

0535783 - MÚ 2022 RIV US eng J - Journal Article
Abbatiello, A. - Feireisl, Eduard - Novotný, A.
Generalized solutions to models of compressible viscous fluids.
Discrete and Continuous Dynamical Systems. Roč. 41, č. 1 (2021), s. 1-28. ISSN 1078-0947. E-ISSN 1553-5231
Institutional support: RVO:67985840
Keywords : compressible fluid * defect measure * dissipative solution * non-homogenous boundary data * non-linear viscous fluid
OECD category: Pure mathematics
Impact factor: 1.588, year: 2021
Method of publishing: Open access
http://dx.doi.org/10.3934/dcds.2020345

We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides with the strong solution as long as the latter exists (weak–strong uniqueness) and they solve the problem in the classical sense as soon as they are smooth (compatibility). We consider general models of compressible viscous fluids with non–linear viscosity tensor and non–homogeneous boundary conditions, for which the problem of existence of global–in–time weak/strong solutions is largely open.
Permanent Link: http://hdl.handle.net/11104/0313717