Abstract
Abstract
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.
Funder
Fundação para a Ciência e a Tecnologia
Russian Science Foundation
Ministry of Education and Science of the Republic of Kazakhstan
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
18 articles.
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