arXiv subjects
Publications and source records attributed to S. N. Antontsev.
An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is established: velocity, density and pressure. Under additional regularity assumptions, we also prove the uniqueness of the solution.
We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions can be written in the form $\mathbf{v}\cdot \mathsf{n}=a,$ $2D(\mathbf{v})\mathsf{n}\cdot \mathsf{s}+α\mathbf{v}% \cdot {\mathsf{s}}=b,$ where the tensor $D(\mathbf{v})$ is the rate-of-strain of the fluid's velocity $\mathbf{v}$ and\ $\mathsf{(n},% \mathsf{s)}$ is the pair formed by the normal and tangent vectors to the boundary. We establish the solvability of this problem in the class of solutions with $L_{p}-$bounded \ vorticity, $p\in (2,\infty ].$ To prove the solvability we realize the passage to the limit in Navier-Stokes equations with vanishing viscosity.
We study a mean-field model of superconducting vortices in a II-type superconductor. We prove the global solvability of the problem about a flux of superconducting vortices through a given domain and also analyse the regularity of weak solutions.