On generalized energy equality of the Navier-Stokes equations.
On global motion of a compressible barotropic viscous fluid with boundary slip condition
Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the -approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to and the density belongs to , α ∈ (1/2,1).
On global regular solutions to the Navier-Stokes equations with heat convection
Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on , we continue the local solutions step by step up to a global one.
On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid.
On interior regularity criteria for weak solutions of the navier-stokes equations.
On L2 Decay of Weak Solutions of the Navier-Stokes Equations in Rn.
On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the -approach the Lagrangian coordinates must be used. We are looking...
On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the -approach, because the velocity belongs to with r > 3.
On minimizers with prescribed divergence
On multiresolution methods in numerical analysis.
On noncompact free boundary problems for the plae stationary Navier-Stokes equations.
On non-homogeneous viscous incompressible fluids. Existence of regular solutions
We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when is smooth enough, there exists a local strong regular solution (which is global for small regular data).
On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface [Book]
On nonstationary Stokes problem in exterior domains
On nonsymmetric two-dimensional viscous flow through an aperture.
On one class of matrix differential operators.
On optimal decay rates for weak solutions to the Navier-Stokes equations in
This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in . Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound
On Optimum Regularity of Navier-Stokes Solutions at Time t = 0.
On questions of decay and existence for the viscous Camassa–Holm equations
On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system
This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.