Related papers: Global-in-time existence of weak solutions for Vla…
This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…
In this paper the global existence of weak solutions to the relativistic BGK model for the relativistic Boltzmann equation is analyzed. The proof relies on the strong compactness of the density, velocity and temperature under minimal…
In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak…
We consider the Fokker-Planck equation with a strong external magnetic field. Global-in-time solutions are built near the Maxwellian, the global equilibrium state for the system. Moreover, we prove the convergence to equilibrium at…
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…
Based on the recent study on the Vlasov-Poisson-Boltzmann system with general angular cutoff potentials [3, 4], we establish in this paper the global existence of classical solutions to the Cauchy problem of the Vlasov-Poisson-Landau system…
The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial…
A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic,…
We prove uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We make use of the Lagrangean framework in comparing the instantaneous states of corresponding fluid particles in two…
This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…
In this paper, we study the hydrodynamic limit of the scaled Vlasov-Poisson-Fokker-Planck (VPFP) system in the low-field regime. By employing the moment method, we formally derive the corresponding Drift-Diffusion-Poisson (DDP) system.…
We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill--posed in the class of weak solutions for a large class of physically admissible data.…
In the present paper, we investigated the gravitational black-hole-hedgehog's solution with magnetic field contribution in the framework of the f(R)--gravity described by the Gravi-Weak unification model. Assuming the Multiple Point…
We investigate the existence and multiplicity of weak solutions for a nonlinear Kirchhoff type quasilinear elliptic system on the whole space $\mathbb{R}^N$. We assume that the nonlinear term satisfies the locally super-$(m_1,m_2)$…
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an…
We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This…
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…
We present a global approach of non-dissipative physics. Based on symplectic mechanics this technique allows us to obtain the solution of a very large class of problems in terms of a Taylor expand. We apply this method to the problem of…
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…
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary…