A time periodic solution of the Navier-Stokes equations with mixed boundary conditions
Conditions for the local regularity of weak solutions of the Navier-Stokes equations near the boundary.
Remark on regularity of weak solutions to the Navier-Stokes equations.
Profesor František Vyčichlo podle archivních pramenů a ve vzpomínkách kolegů a žáků
Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations
In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.
A note on the generalized energy inequality in the Navier-Stokes equations
We prove that there exists a suitable weak solution of the Navier-Stokes equation, which satisfies the generalized energy inequality for every nonnegative test function. This improves the famous result on existence of a suitable weak solution which satisfies this inequality for smooth nonnegative test functions with compact support in the space-time.
An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions
The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends...
Remark on regularity of weak solutions to the Navier-Stokes equations
Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space are regular.
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