Related papers: Global weak solutions to compressible quantum Navi…
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…
We consider the compressible Vlasov-Poisson-Fokker-Planck-Navier-Stokes system in a three dimensional bounded domain with nonhomogeneous Dirichlet boundary conditions. The system describes the evolution of charged particles ensemble…
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,…
We consider the Quantum Navier-Stokes system in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. The main novelties are that vacuum regions are included in the weak formulation and no…
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…
We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are…
In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…
We introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $\dot{B}^{-1+\frac{3}{p}}_{p,\infty}$, $p > 3$. These solutions satisfy a certain…
A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…
This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…
We consider a dissipative quantum fluid on the whole space $\mathbb{R}^d$ ($d\geq 1$) confined by an external harmonic potential. The dynamics of the quantum fluid is described by the Quantum Navier-Stokes (QNS) system which is a particular…
We study the anisotropic, incompressible Cahn-Hilliard-Navier-Stokes system with variable density in a bounded smooth domain $\Omega \subset \mathbb{R}^d$. This work extends previous results on the isotropic case by incorporating…
In this paper, we prove global existence of weak solutions for the stationary compressible Navier-Stokes equations with an anisotropic and nonlocal viscous term in a periodic domain. This gives an answer to an open problem important for…
We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…
We establish the global existence of weak solutions to the isentropic compressible Navier-Stokes equations in three-dimensional annular cylinders with Navier-slip boundary conditions, allowing large axisymmetric initial data and vacuum…
This paper proves existence of a global weak solution to the inhomogeneous (i.e., non-constant density) incompressible Navier-Stokes system with mass diffusion. The system is well-known as the Kazhikhov-Smagulov model. The major novelty of…
We explore the existence of global weak solutions to the Hookean dumbbell model, a system of nonlinear partial differential equations that arises from the kinetic theory of dilute polymers, involving the unsteady incompressible…
The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution…
In this work we consider the generalized Navier-Stoke equations with the presence of a damping term in the momentum equation. % The problem studied here derives from the set of equations which govern the isothermal flow of incompressible,…