Strong solutions for the Navier-Stokes-Voigt equations with non-negative density
de Oliveira H.B. Khompysh K. Shakir A.G.
1 April 2025American Institute of Physics
Journal of Mathematical Physics
2025#66Issue 4
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated nonlinear initial-and boundary-value problem, we prove the global-in-time existence of strong solutions (velocity, density and pressure). We also establish some other regularity properties of these solutions and find the conditions that guarantee the uniqueness of velocity and density. The main novelty of this work is the hypothesis that, in some subdomain of space, there may be a vacuum at the initial moment, that is, the possibility of the initial density vanishing in some part of the space domain.
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FCT-Universidade do Algarve, Faro, Portugal
CIDMA, Universidade de Aveiro, Aveiro, Portugal
Al-Farabi Kazakh National University, Almaty, Kazakhstan
FCT-Universidade do Algarve
CIDMA
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026