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.
On recent progress for the stochastic Navier Stokes equations
We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity, exponential...
On regularity of stationary solutions to the Navier-Stokes equation in 3D torus.
On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a cone.
On solvability of the Stokes problem in Sobolev power weight spaces
On some free boundary problems for Navier-Stokes equations
In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.
On some free boundary problems for the Navier-Stokes equations with moving contact points and lines.
On spatial decay estimates for derivatives of vorticities of the two dimensional Navier-Stokes flow
On stability of axially symmetric solutions to Navier-Stokes equations in a cylindrical domain and with boundary slip conditions
The existence of global regular axially symmetric solutions to Navier-Stokes equations in a bounded cylinder and for boundary slip conditions is proved. Next, stability of these solutions is shown.
On steady compressible Navier-Stokes equations in plane domains with corners.
On steady motion of a drop in an infinite liquid medium
On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas.
On the behavior of a nonstationary Poiseuille solution as .
On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
On the blow up criterion for the 2-D compressible Navier-Stokes equations
Motivated by [10], we prove that the upper bound of the density function controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.