On a possibility of generalization of the Hopf lemma to the case of the Navier-Stokes system with nonzero flows.
On a problem of shallow water type.
On a steady flow in a three-dimensional infinite pipe
The paper examines the steady Navier-Stokes equations in a three-dimensional infinite pipe with mixed boundary conditions (Dirichlet and slip boundary conditions). The velocity of the fluid is assumed to be constant at infinity. The main results show the existence of weak solutions with no restriction on smallness of the flux vector and boundary conditions.
On an estimate for the linearized compressible Navier-Stokes equations in the -framework
An -estimate with a constant independent of time for solutions of the linearized compressible Navier-Stokes system in the whole space (under the assumption that solutions have compact supports in space) is obtained.
On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain
This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of estimates for the Stokes semigroup associated with a linearized problem, which is also...
On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations [Book]
On approximate controllability of the Stokes system
On Asymptotic Behavior of Solution for the Navier-Stokes Equations in a Time Dependent Domain.
On axially symmetric flows in .
On backward-time behavior of the solutions to the 2-D space periodic Navier–Stokes equations
On Bardina and Approximate Deconvolution Models
We first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution”...
On bounded solutions of one-dimensional compressible Navier-Stokes equations
On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable
We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant .
On dynamics of fluids in meteorology
We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.
On Energy Inequality, Smoothness and Large Time Behavior in L2 for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations.
On evolution inequalities of a modified Navier-Stokes type. III
This is the last from a series of three papers dealing with variational equations of Navier-Stokes type. It is shown that the theoretical results from the preceding parts (existence and regularity of solutions) can be applied to the problem of motion of a fluid through a tube.
On evolution inequalities of a modified Navier-Stokes type. I
The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.
On evolution inequalities of a modified Navier-Stokes type. II
The present part of the paper continues the study of the abstract evolution inequality from the first part. Theorem 1 states the existence and uniqueness of a weak solution to the evolution inequality under consideration. The proof is based on the method of approximation of the weak solution by a sequence of strong solutions. Theorem 2 yields two regularity results for the strong solution.
On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions
In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity polynomially increasing with a scalar quantity that evolves according to an evolutionary convection diffusion equation with the right hand side that is merely -integrable over space and time. We also formulate a conjecture concerning regularity...