The classical Kelvin-Voigt problem for incompressible fluids with unknown non-constant density: Existence, uniqueness and regularity
Antontsev S.N. De Oliveira H.B. Khompysh K.
May 2021IOP Publishing Ltd
Nonlinearity
2021#34Issue 53083 - 3111 pp.
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.
existence , incompressible fluids with non-constant density , Kelvin-Voigt equations , regularity , uniqueness
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CMAF CIO, Universidade de Lisboa, Portugal
Lavrentyev Institute of Hydrodynamics, SB RAS, Novosibirsk, Russian Federation
FCT, Universidade Do Algarve, Faro, Portugal
Al-Farabi Kazakh National University, Almaty, Kazakhstan
CMAF CIO
Lavrentyev Institute of Hydrodynamics
FCT
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
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