Lie group analysis of magnetohydrodynamic flow and mass transfer of a visco-elastic fluid over a porous stretching sheet.
Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids
The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
Local existence of the solution to the initial-boundary value problem in nonlinear thermodiffusion in micropolar medium.
Localization and Blow-Up of Thermal Waves in Nonlinear Heat Conduction with Peaking.
Long time existence of solutions to 2d Navier-Stokes equations with heat convection
Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that , , s>2.