Related papers: Dissipative structures in compressible inviscid fl…
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of…
Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle…
In this paper, we consider the energy decay of a damped hyperbolic system of wave-wave type which is coupled through the velocities. We are interested in the asymptotic properties of the solutions of this system in the case of indirect…
We establish local balance equations for smooth functions of the vorticity in the DiPerna-Majda weak solutions of 2D incompressible Euler, analogous to the balance proved by Duchon and Robert for kinetic energy in 3D. The anomalous term or…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the…
We identify a class of measure-valued solutions of the barotropic Euler system on a general (un-bounded) spatial domain as a vanishing viscosity limit for the compressible Navier-Stokes system. Then we establish the weak…
We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that when the…
We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy…
The basic model for incompressible two-phase flows with phase transitions is derived from basic principles and shown to be thermodynamically consistent in the sense that the total energy is conserved and the total entropy is nondecreasing.…
We analyze the Ericksen-Leslie system equipped with the Oseen-Frank energy in three space dimensions. The new concept of dissipative solutions is introduced. Recently, the author introduced the concept of measure-valued solutions to the…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
We formulate a thermodynamically consistent continuum theory for compressible, viscous, heat-conducting fluids in which the velocity entering the balance of mass is distinguished from the specific linear momentum entering the balances of…
A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dissipation of positive solutions is proved and decay of energy like $t^{-2}$ is established.…
We present an overview of recent developments on the convergence analysis of numerical methods for inviscid multidimensional compressible flows that preserve underlying physical structures. We introduce the concept of generalized solutions,…
We present simulations of coherent structures in compressible flows near the transition to turbulence using the Dissipative Particle Dynamics (DPD) method. The structures we find are remarkably consistent with experimental observations and…
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. The underlying relative energy inequality holds as an equality for classical solutions and if the additional variable vanishes, these…
We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the…
We show the relative energy inequality for the compressible Navier-Stokes system driven by a stochastic forcing. As a corollary, we prove the weak-strong uniqueness property (pathwise and in law) and convergence of weak solutions in the…
So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…
We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes equations, we prove…