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Strong solutions to the Navier-Stokes equations on thin 3D domains
B. Nowakowski, W. Zajączkowski
We prove the existence of strong solutions to Navier-Stokes equations in three dimensional thin domains. Our proof is based on the energy and the Poincaré inequalities as well as c…
Very weak solutions to the boundary-value problem of the homogenous heat equation
B. Nowakowski, W. Zajączkowski
We consider the homogeneous heat equation in a domain in with vanishing initial data and the Dirichlet boundary condition. We are looking for solutions in $W^{r,…
Long time existence of regular solutions to non-homogeneous Navier-Stokes equations
Wojciech M. Zajaczkowski
We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that th…
Existence of global weak solutions for Navier-Stokes equations with large flux
Joanna Renclawowicz, Wojciech Zajaczkowski
Global existence of weak solutions to the Navier-Stokes equation in a cylindrical domain under the slip boundary conditions and with inflow and outflow was proved. To prove the ene…