Wojciech M. Zajączkowski

On a Lp-estimate for the linearized compressible Navier–Stokes equations with the Dirichlet boundary conditions☆

Abstract In this paper a special L p -estimate for the linearized compressible Navier–Stokes in the Lagrangian coordinates for the Dirichlet boundary conditions is obtained. The constant in the estimate does not depend on the length of time interval [0, T ]. The result is essential to obtain an existence for regular solutions for the nonlinear problem with the lowest class of regularity in L p -spaces.

Remarks on regularity criteria for axially symmetric weak solutions to the Navier–Stokes equations

We examine the conditional regularity of the solutions to the Navier–Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if a radial or angular component of velocity satisfies a weighted Serrin condition, then the solution is regular. Copyright

Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry

Global existence of regular solutions to the Navier-Stokes equations in a bounded cylindrical domain without the axis of symmetry and with boundary slip conditions is proved. We showed the existence of solutions without restrictions on the magnitude of the initial velocity assuming only that the

Large time regular solutions to the Navier-Stokes equations in cylindrical domains

L_2

Global regular solutions to the Navier-Stokes equations in an axially symmetric domain

-norms of the angular derivative of the cylindrical components of the initial velocity and the external force are sufficiently small. To prove global existence some decay estimates on the external force are imposed.

Global axially symmetric solutions with large swirl to the Navier-Stokes equations

We prove the large time existence of solutions to the Navier-Stokes equations with slip boundary conditions in a cylindrical domain. Assuming smallness of

Existence and stability theorems for abstract parabolic equations, and some of their applications

L_2

Weak solutions to 3-D Cahn-Hilliard system in elastic solids

-norms of derivatives of initial velocity with respect to variable along the axis of the cylinder, we are able to obtain estimate for velocity in

Olga Alexandrovna Ladyzhenskaya

W^{2,1}_2

On Global Existence of Solutions of the Neumann Problem for Spherically Symmetric Nonlinear Viscoelasticity in a Ball

without restriction on its magnitude. Then existence follows from the Leray-Schauder fixed point theorem.