Related papers: Maximal dissipative solutions for incompressible f…
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The…
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure…
Note that some classic fluid dynamical systems such as the Navier-Stokes equations, Magnetohydrodynamics (MHD), Boussinesq equations, and etc are observably different from each other but obey some energy inequalities of the similar type. In…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
We consider the compressible Navier-Stokes system where the viscosity depends on density and the heat conductivity is proportional to a positive power of the temperature under stress-free and thermally insulated boundary conditions. Under…
We study in the inviscid limit the global energy dissipation of Leray solutions of incompressible Navier-Stokes on the torus ${\mathbb T}^d$, assuming that the solutions have norms for Besov space $B^{\sigma,\infty}_3({\mathbb T}^d),$…
In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…
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…
This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…
We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…
New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of…
We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different…
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler…
This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…
We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…
We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this…
We propose a novel version of the dissipative Gross--Pitaevski equation and examine its properties. In contrast to previous proposals our approach, based on the metriplectic formulation of the dissipative system dynamics, conserves the…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
We present a new family of exact solutions of dissipative fireball hydrodynamics for arbitrary bulk and shear viscosities. The main property of these solutions is a spherically symmetric, Hubble flow field. The motivation of this paper is…
This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…