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This study investigates the role of thermal boundary conditions on natural convection and entropy generation in non-Newtonian power-law fluids confined within a square cavity and a concentric cylindrical annulus. Steady, two-dimensional…
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0,…
We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this…
We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…
We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…
We study and develop constraint preserving boundary conditions for the Newtonian magnetohydrodynamic equations and analyze the behavior of the numerical solution upon considering different possible options.
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations…
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
Thermocapillary convection is particularly effective for the control of thin liquid film topography or for the actuation of microparticles at the liquid-air interface. Experiments with water are challenging, however, as its interface is…
The question on expansion of moving volume inside of a smooth flow of the compressible liquid is under consideration. We find a condition on initial data such that if it holds, then within a finite time either the boundary of the moving…
We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with…
The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After…
Recently, Kaladze and Misra [Phys. Scr. 99 (2024) 085013] showed that the tropospheric stratified fluid flows may be unstable by the effects of the negative temperature gradient and the temperature-dependent density inhomogeneity arising…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…