Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLow Mach number limit of full compressible Navier-Stokes equations with revised Maxwell law
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we study the low Mach number limit of the full compressible Navier-Stokes equations with revised Maxwell law. By applying the uniform estimation of the error system, we prove that the solutions of the full compressible Navier-Stokes equations with time relaxation converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.
rate research
Read More
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 $rho to infty$. This solution is obtained as the vanishing viscosity limit of classical solutions of the one-dimensional, isentropic, compressible Navier--Stokes equations. Our approach relies on the method of compensated compactness to pass to the limit rigorously in the nonlinear terms. Key to our strategy is the derivation of hyperbolic representation formulas for the entropy kernel and related quantities; among others, a special entropy pair used to obtain higher uniform integrability estimates on the approximate solutions. Intricate bounding procedures relying on these representation formulas then yield the required compactness of the entropy dissipation measures. In turn, we prove that the Young measure generated by the classical solutions of the Navier--Stokes equations reduces to a Dirac mass, from which we deduce the required convergence to a solution of the Euler equations.
The energy equalities of compressible Navier-Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient conditions on the regularity of weak solutions for these equalities to hold. The method of proof is suitable for the case of periodic as well as homogeneous Dirichlet boundary conditions. In particular, by a careful analysis using the homogeneous Dirichlet boundary condition, no boundary layer assumptions are required when dealing with bounded domains with boundary.
In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier-Stokes equations, we improve almost all the blow up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier-Stokes equations. Enlightening regular criteria via pressure $Pi=frac{text {divdiv}}{-Delta}(u_{i}u_{j})$ of the 3D incompressible Navier-Stokes equations on bounded domain, we generalize Beirao da Veigas result in [1] from the incompressible Navier-Stokes equations to the isentropic compressible Navier-Stokes system in the case away from vacuum.
In this paper, we derive several new sufficient conditions of non-breakdown of strong solutions for for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations. First, it is shown that there exists a positive constant $varepsilon$ such that the solution $(rho,u,theta)$ to full compressible Navier-Stokes equations can be extended beyond $t=T$ provided that one of the following two conditions holds (1) $rho in L^{infty}(0,T;L^{infty}(mathbb{R}^{3}))$, $uin L^{p,infty}(0,T;L^{q,infty}(mathbb{R}^{3}))$ and $$| u|_{L^{p,infty}(0,T;L^{q,infty}(mathbb{R}^{3}))}leq varepsilon, ~~text{with}~~ {2/p}+ {3/q}=1, q>3;$$ (2) $lambda<3mu,$ $rho in L^{infty}(0,T;L^{infty}(mathbb{R}^{3}))$, $thetain L^{p,infty}(0,T;L^{q,infty}(mathbb{R}^{3}))$ and $$|theta|_{L^{p,infty}(0,T; L^{q,infty}(mathbb{R}^{3}))}leq varepsilon, ~~text{with}~~ {2/p}+ {3/q}=2, q>3/2.$$ To the best of our knowledge, this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid. Second, we establish some blow-up criteria in anisotropic Lebesgue spaces to the full Navier-Stokes system. Third, without the condition on $rho$ in (0.1) and (0.3), the results also hold for the 3D nonhomogeneous incompressible Navier-Stokes equations. The appearance of vacuum in these systems could be allowed.
We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singularity do to cavitation at the origin.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
