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We present a blow-up result for large data for relaxed compressible Navier-Stokes models avoiding the possibility of reaching the boundary of hyperbolicity. Thus a previous result is improved and further examples are given illustrating…
In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near…
We study an initial boundary value problem for the 3-dimensional compressible Navier-Stokes equations with hyperbolic heat conduction, where the classical Fourier law is replaced by the Cattaneo-Christov constitutive relation. We focus on…
We study the global existence and uniqueness of classical solutions to the three-dimensional compressible isentropic Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large provided the initial…
We study the 1D Brenner-Navier-Stokes-Fourier (BNSF) system, proposed as a refinement of the classical Navier--Stokes--Fourier model through the introduction of the volume velocity, distinct from the mass velocity describing convective…
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…
This paper studies local existence and the singularity formation of the solutions of the one-dimensional hyperbolic Navier-Stokes equations, in particular proving the gradient blow-up of the derivatives of the solutions. The underlying…
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…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the…
We are concerned with the global existence of classical solutions to the barotropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. We demonstrate that the classical solutions…
In this paper we consider the Cauchy problem for the 3D Navier-Stokes equations for incompressible flows. The initial data are assumed to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solutions can…
For periodic initial data with initial density allowed to vanish, we establish the global existence of strong and weak solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity…
First of all, we get the global existence of classical and strong solutions of the full compressible Navier-Stokes equations in three space dimensions with initial data which is large and spherically or cylindrically symmetric. The…
We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional barotropic compressible quantum Navier-Stokes equations, which consists of the compressible…
This work is concerned with the global existence of large solutions to the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible…
In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…
We study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up…