Related papers: Analysis of a thermodynamically consistent Navier-…
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 classical initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular (e.g., logarithmic) potential. We prove that any weak solution converges to a single equilibrium using…
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…
The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure…
We consider the Hookean dumbbell model, a system of nonlinear PDEs arising in the kinetic theory of homogeneous dilute polymeric fluids. It consists of the unsteady incompressible Navier-Stokes equations in a bounded Lipschitz domain,…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
We construct solutions to the randomly-forced Navier--Stokes--Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense…
We present the first generalization of Navier-Stokes theory to relativity that satisfies all of the following properties: (a) the system coupled to Einstein's equations is causal and strongly hyperbolic; (b) equilibrium states are stable;…
We study the long-time behaviour of a stochastic Allen-Cahn-Navier-Stokes system modelling the dynamics of binary mixtures of immiscible fluids. The model features two stochastic forcings, one on the velocity in the Navier-Stokes equation…
We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…
We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the…
This work is based on a formulation of the incompressible Navier-Stokes equations developed by P. Constantin and G.Iyer, where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. If…
In this paper we prove the existence of global strong solution for the Navier-Stokes equations with general degenerate viscosity coefficients. The cornerstone of the proof is the introduction of a new effective pressure which allows to…
We study the large-time behavior of strong solutions to the one-dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity is proportional…
We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…
We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain $R^d (d = 2, 3)$, provided…
A new system of general Navier-Stokes-like equations is proposed to model electromagnetic analogous to hydrodynamic. While most attempts to derive analogues of hydrodynamic to electromagnetic, and vice-versa, start with Navier-Stokes or a…
In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the…
In this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and…
We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved…