TY  - JOUR
T1  - On a class of compressible viscoelastic rate-type fluids with stress--diffusion
A1  - Bulíček, Miroslav
A1  - Feireisl, Eduard
A1  - Málek, Josef
JA  - Nonlinearity
Y1  - 2019
VL  - 32
IS  - 12
SP  - 4665
EP  - 4681
M2  - doi: 10.1088/1361-6544/ab3614
KW  - Compressible fluid
KW  - global--in--time existence
KW  - non-Newtonian fluid
KW  - stress diffusion
KW  - viscoelastic fluid
KW  - weak solution
N2  - We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids with stress diffusion. Our approach is based on the concepts used
in the nowadays standard theory of compressible Newtonian fluids as renormalization, effective viscous flux identity, compensated compactness. The presence
of the extra stress, however, requires substantial modification of these techniques, in particular, a new version of the effective viscous flux identity is derived.
With help of these tools, we show the existence of global--in--time weak solutions for any finite energy initial data.
M1  - Preprint project = NCMM
M1  - Preprint year = 2018
M1  - Preprint number = 10
M1  - Preprint ID = NCMM/2018/10
ER  -