Related papers: Spatially-Periodic Solutions for Evolution Anisotr…
In this paper we consider evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under Rauch…
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically…
This paper is devoted to proving the existence of time-periodic solutions of one-phase or two-phase problems for the Navier-Stokes equations with small periodic external forces when the reference domain is close to a ball. Since our…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…
We investigate weak Serrin-type blowup criterion of the three-dimensional full compressible Navier-Stokes equations for the Cauchy problem, Dirichlet problem and Navier-slip boundary condition. It is shown that the strong or smooth solution…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…
In this note, by constructing suitable approximate solutions, we prove the existence of global weak solutions to the compressible Navier-Stokes equations with density-dependent viscosity coefficients in the whole space $\mathbb{R}^N$,…
In this paper, we study the stochastic-periodic homogenization of Non-stationary Navier-Stokes Type Equations on anisotropic heterogeneous media. More precisely, we are interested in the stochastic-periodic homogenization of its variational…
We extend the well-known Serrin's blowup criterion for the three-dimensional (3D) incompressible Navier-Stokes equations to the 3D viscous compressible cases. It is shown that for the Cauchy problem of the 3D compressible Navier-Stokes…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
We consider coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as…
This paper is concerned with the existence, uniqueness and time-asymptotic stability of time periodic solutions to the compressible Navier-Stokes-Korteweg system effected by a time periodic external force in $\mathbb{R}^n$. Our analysis is…
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…
Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimension $n\geq 2$ are investigated. Integrability properties and pointwise estimates are established.
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
In this paper, we develop a novel enriched Galerkin (EG) method for the steady incompressible Navier-Stokes equations in rotational form, which is both pressure-robust and parameter-free. The EG space employed here, originally proposed in…
In this paper we prove nonexistence of stationary weak solutions to the Euler-Poisson equations and the Navier-Stokes-Poisson equations in $\Bbb R^N$, $N\geq 2$, under suitable assumptions of integrability for the density, velocity and the…
We present a variational approach for the construction of Leray-Hopf solutions to the non-Newtonian Navier-Stokes system. Inspired by the work [42] on the corresponding Newtonian problem, we minimise certain stabilised Weighted…
The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…