The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity

The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity Full article

Journal

Nonlinearity
ISSN: 0951-7715

Output data

Year: 2021, Volume: 34, Number: 5, Pages: 3083-3111 Pages count : 29 DOI: 10.1088/1361-6544/abe51e

Tags

existence; incompressible fluids with non-constant density; Kelvin-Voigt equations; regularity; uniqueness

Authors

Antontsev S N ^1,2 , de Oliveira H B ^1,3 , Khompysh Kh ⁴

Affiliations

1	CMAF CIO—Universidade de Lisboa, Portugal
2	Lavrentyev Institute of Hydrodynamics, SB RAS, Novosibirsk, Russia
3	FCT—Universidade do Algarve, Faro, Portugal
4	Al-Farabi Kazakh National University, Almaty, Kazakhstan

The classical Kelvin-Voigt equations for incompressible fluids with non-constant density are investigated in this work. To the associated initial-value problem endowed with zero Dirichlet conditions on the assumed Lipschitz-continuous boundary, we prove the existence of weak solutions: velocity and density. We also prove the existence of a unique pressure. These results are valid for d ∈ {2, 3, 4}. In particular, if d ∈ {2, 3}, the regularity of the velocity and density is improved so that their uniqueness can be shown. In particular, the dependence of the regularity of the solutions on the smoothness of the given data of the problem is established.

Antontsev S.N. , de Oliveira H.B. , Khompysh K.
The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity
Nonlinearity. 2021. V.34. N5. P.3083-3111. DOI: 10.1088/1361-6544/abe51e WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000649646700001
Scopus:	2-s2.0-85107079212
Elibrary:	46783101
OpenAlex:	W3162093851

DB	Citing
Scopus	18
OpenAlex	22
Elibrary	25
Web of science	19