Strong solutions to the Navier-Stokes-Fourier system with slip-inflow boundary conditions [PDF]
arXiv, 2012 We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution provided the data are close to a constant, but nontrivial flow with sufficiently large dissipation in the energy ...
arxiv
Steady 3D viscous compressible flows with adiabatic exponent $γ\in (1,\infty)$ [PDF]
arXiv, 2013 The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak solution under the assumption that the adiabatic exponent satisfies $\gamma>1$ is proved. These results cover the
arxiv
Time-periodic solutions to the full Navier--Stokes--Fourier system with radiation on the boundary [PDF]
arXiv, 2014 The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following sense: we extend the class of pressure functions (i.e.
arxiv
Global well-posedness for Euler-Nernst-Planck-Possion system in dimension two [PDF]
arXiv, 2014 In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion system. We obtain global well-posedness for the system in dimension $d=2$ for any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)$ under certain conditions of $s_1$ and $s_2$.
arxiv
Isothermal Navier-Stokes Equations and Radon Transform [PDF]
arXiv, 2014 In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a problem with no-slip condition for nonstationary motion of viscous compressible isothermal fluid.
arxiv
The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions [PDF]
arXiv, 2014 We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity parameters when these are small. These solutions then converge globally and strongly in $L^2$ towards the solution of
arxiv
Global solvability of 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity [PDF]
arXiv, 2015 In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla u_0\|_{L^2}$ is suitably small with arbitrary large initial density.
arxiv
Local existence of strong solutions to the $k-\varepsilon$ model equations for turbulent flows [PDF]
arXiv, 2015 In this paper, we are concerned with the local existence of strong solutions to the $k-\varepsilon$ model equations for turbulent flows in a bounded domain $\Omega$$\subset$ $\mathbb{R}^{3}$. We prove the existence of unique local strong solutions under the assumption that turbulent kinetic energy and the initial density both have lower bounds away ...
arxiv
On weak-strong uniqueness property for full compressible magnetohydrodynamics flows
Open Mathematics, 2013 Yan Weiping
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Partial regularity of solution to generalized Navier-Stokes problem
Open Mathematics, 2014 Mácha Václav
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