Related papers: Inhomogeneous incompressible viscous flows with sl…
In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…
The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…
The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent…
We prove that the solutions to the 3D Navier-Stokes equation with constant rotation exist globally for small axisymmetric initial data, where the smallness is uniform with respect to the viscosity $\nu \in [0,\infty)$. This expands the work…
In this paper, we present a new framework for the global well-posedness and large-time behavior of a two-phase flow system, which consists of the pressureless Euler equations and incompressible Navier-Stokes equations coupled through the…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…
In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone…
We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…
We investigate the global unique Fujita-Kato solution to the 3-D inhomogeneous incompressible Navier-Stokes equations with initial velocity $u_0$ being sufficiently small in critical spaces and with initial density being bounded from above…
This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous…
We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has…
The small data global well-posedness of the 3D incompressible Navier-Stokes equations in $\mathbb R^3$ with only one-directional dissipation remains an outstanding open problem. The dissipation in just one direction, say $\partial_1^2 u$ is…
Adding some nontrivial terms composed from a microstructure, we prove the existence of a global-in-time weak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier-Stokes-Fourier system for arbitrary initial…
In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension $d= 2,3$. The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and $H^{1}$…
This paper is devoted to the study of the Cauchy problem for the stratified Navier-Stokes system in space dimension three. In the first part of the paper, we prove the existence of a unique global solution $(v_\nu,\rho_\nu)$ for this system…
In this paper, we study the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain excluding the axis. We establish the global existence and exponential decay of weak,…