Related papers: On the Cauchy problem for the multi-dimensional co…
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…
In this paper we investigate well-posedness of the Cauchy problem of the three dimensional generalized Navier-Stokes system. We first establish local well-posedness of the GNS system for any initial data in the Fourier-Herz space…
We consider the global well-posedness of the inhomogeneous incompressible Navier-Stokes-Korteweg system with a general capillary term. Based on the maximal regularity property, we obtain the global existence and uniqueness of solutions to…
We consider Navier-Stokes equations for compressible viscous fluids in the one-dimensional case with general viscosity coefficients. We prove the existence of global weak solution when the initial momentum $\rho_0 u_0$ belongs to the set of…
We consider the one-dimensional compressible Navier--Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity $\mu$ and the heat conductivity $\kappa$ depend on the specific volume $v$ and the temperature…
In this paper, we study the global regularity of strong solution to the Cauchy problem of 3D incompressible Navier-Stokes equations with large data and non-zero force. We prove that the strong solution exists globally for $\nabla u\in…
In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution of this paper…
In this paper, the main objective is to generalize to the Navier-Stokes-Korteweg (with density dependent viscosities satisfying the BD relation) and Euler-Korteweg systems a recent relative entropy [proposed by D. Bresch, P. Noble and…
The formation of singularity and breakdown of strong solutions to the two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction are considered. It is shown that for the initial density…
In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived…
This paper investigates the Cauchy problem for the compressible pressureless Navier-Stokes system in $\mathbb{R}^d$ with $d \geq 2$. Unlike the standard isentropic compressible Navier-Stokes system, the density in the pressureless model…
In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of…
In this paper, the Cauchy problem for a one-dimensional heat conducting compressible non-Newtonian fluid is considered. The constitute equation of the non-Newtonian fluid is determined by two nonlinear terms $(|u_x|^{q-2}u_x)_x$ and…
In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier-Stokes equations (STCNS, for short). Our main goal…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…
We investigate compressible nematic liquid crystal flows in three-dimensional (3D) bounded domains with slip boundary condition for velocity and Neumann boundary condition for orientation field. By applying piecewise-estimate method and…
The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is…
We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space $BMO^{-1}$ from which there exist two distinct global solutions, both smooth for all $t>0$.…
In this paper, we investigate the existence of a global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum. Precisely, when the far-field density is vacuum…