Related papers: The global well-posedness for the compressible flu…
In this paper, we consider the compressible fluid model of Korteweg type in a critical case where the derivative of pressure equals to $0$ at the given constant state. It is shown that the system admits a unique, global strong solution 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…
This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We distinguish two cases,…
This work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We will prove the existence…
The global solutions with large initial data for the isothermal compressible fluid models of Korteweg type has been studied by many authors in recent years. However, little is known of global large solutions to the nonisothermal…
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…
Let us consider the $3$D compressible Navier--Stokes--Korteweg system in the rotational framework. Although there is a wealth of literature on the weak solutions to this system, there seem to be no results on the strong solutions. In this…
We consider the isentropic Navier-Stokes-Korteweg equations with a non-decreasing pressure on the whole space $\mathbb{R}^n$ $(n \ge 2)$, where the system describes the motion of compressible fluids such as liquid-vapor mixtures with phase…
This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) \cite{3DS}, which can be used as a phase transition model. We distinguish two…
This paper studies the one dimensional Navier-Stokes-Fourier-Korteweg system of equations describing the evolution of a heat-conducting compressible fluid that exhibits viscosity and capillarity. The main goal of the present analysis is to…
Global existence of solutions to the compressible Navier-Stokes-Korteweg system around a constant state is studied. This system describes liquid-vapor two phase flow with phase transition as diffuse interface model. In previous works they…
In this work, we establish the global existence of strong solutions to the 2D and 3D compressible Navier-Stokes-Korteweg system with arbitrarily large initial data on the torus. This system was derived by Dunn and Serrin [Arch. Ration.…
We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The…
This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5]…
In this paper, we mainly study the global strong solutions and its long time decay rates of all order spatial derivatives to a micro-macro model for compressible polymeric fluids with small initial data. This model is a coupling of…
This work is devoted to the global existence of weak solution for a general isothermal model of capillary fluids derived by C. Rohde, which can be used as a phase transition model. This article is structured in the following way: first of…
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N=2. We address the question of the global existence of strong solutions with large initial data for compressible Navier-Stokes system and Korteweg…
This work is devoted to prove the existence of global strong solution in dimension $N\geq 2$ for a isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see \cite{fDS}), which can be used as a phase transition model.…
Since the pioneering work of Korteweg (1901) and the subsequent refinement of capillary fluid models by Dunn and Serrin (1985), the global existence of strong solutions to the multi-dimensional compressible Navier-Stokes-Korteweg (NSK)…
In this paper we consider the Cauchy problem to the Korteweg system with the general pressure in dimension $d\geq2$, and establish the global well-posedness of strong solution for the small initial data in $L^p$ type critical Besov spaces…