Related papers: Global strong solution to the inviscid liquid-gas …
The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close…
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…
In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main…
This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…
We consider the large time behavior of global strong solutions to the compressible viscoelastic flows on the whole space $\mathbb{R}^N\,(N\geq 2)$, where the system describes the elastic properties of the compressible fluid. Adding a…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…
In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
In this paper, we deal with some Oldroyd type models, which describe incompressible viscoelastic fluids. There are 3 parameters in these models: the viscous coefficient of fluid $\nu_{1}$, the viscous coefficient of the elastic part of the…
We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid and then phase transitions can be taken into consideration;…
We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the $2$D velocity field is space-time…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and…
The global existence of weak solutions of the incompressible viscoelastic flows in two spatial dimensions has been a long standing open problem, and it is studied in this paper. We show the global existence if the initial deformation…
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov…
In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for…
We are concerned with a system of equations in $\mathbb{R}^{d}(d\geq2)$ governing the evolution of isothermal, viscous and compressible fluids of Korteweg type, that can be used as a phase transition model. In the case of zero sound speed…