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IIn the paper, we consider the inviscid, incompressible and semiclassical limits limits of the barotropic quantum Navier-Stokes equations of compressible flows in a periodic domain. We show that the limit solutions satisfy the incompressible Euler system based on the relative entropy inequality and on the detailed analysis for general initial data. The rate of convergence is estimated in terms of the Mach number.
In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $dot{H}^{-alpha}(mathbb{R}^{3})$ or $dot{H}^{-alpha}(mathbb{T}^{3})$ with $0<alphaleq 1/2$. This is ac
We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function
We prove the existence of relative finite-energy vanishing viscosity solutions of the one-dimensional, isentropic Euler equations under the assumption of an asymptotically isothermal pressure law, that is, $p(rho)/rho = O(1)$ in the limit $rho to inf
We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as