Stabilizing influence of a Skew-symmetric operator in semilinear parabolic equation
Navierovy-Stokesovy rovnice: regularita nebo „blow-up‟?
A contribution to the theory of stability of differential equations in Banach space
The linearized uniform asymptotic stability of evolution differential equations
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation
A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
We deal with a suitable weak solution to the Navier-Stokes equations in a domain . We refine the criterion for the local regularity of this solution at the point , which uses the -norm of and the -norm of in a shrinking backward parabolic neighbourhood of . The refinement consists in the fact that only the values of , respectively , in the exterior of a space-time paraboloid with vertex at , respectively in a ”small” subset of this exterior, are considered. The consequence is that...
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity
We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.
Estimates up to the boundary of a weak solution to the Navier-Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor
We formulate sufficient conditions for regularity up to the boundary of a weak solution v in a subdomain Ω × (t₁,t₂) of the time-space cylinder Ω × (0,T) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that Ω is a cube.
Sixtieth anniversary of birthday of Professor Jan Polášek
Zprávy. Životní jubileum prof. RNDr. Jana Poláška, DrSc.
Global weak solvability to the regularized viscous compressible heat conductive flow
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.
Замечание к устойчивости решений уравнения колебания стержня
Destabilizing effect of unilateral conditions in reaction-diffusion systems
Axisymmetric flow of Navier-Stokes fluid in the whole space with non-zero angular velocity component
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.
The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid
The dimension of a set of singularities of weak solutions to the Navier-Stokes equations
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