Semiflow selection for the compressible Navier-Stokes system
Danica Basarić
备注：
typos corrected, Sections 3 and 4.1 rearranged, reference added, results unchanged. arXiv admin note: text overlap with arXiv:1901.04798 by other authors
Although the existence of dissipative weak solutions for the compressible Navier-Stokes system has already been established for any finite energy initial data, uniqueness is still an open problem. The idea is then to select a solution satisfying the semigroup property, an important feature of systems with uniqueness. More precisely, we are going to prove the existence of a semiflow selection in terms of the three state variables: the density, the momentum and the energy. Finally, we will show that it is possible to introduce a new selection defined only in terms of the initial density and momentum; however, the price to pay is that the semigroup property will hold almost everywhere in time.
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In this paper, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable "pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.
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In this paper we study a vanishing pressure process for highly compressible Navier-Stokes equations as the Mach number tends to infinity. We first prove the global existence of weak solutions for the pressureless system in the framework [Li-Xin, arXiv:1504.06826v2], where the weak solutions are established for compressible Navier-Stokes equations with degenerate viscous coefficients. Furthermore, a rate of convergence of the density in $L^{\infty}\left(0,T;L^{2}(\rr)\right)$ is obtained, in case when the velocity corresponds to the gradient of density at initial time.
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We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partialΩ.$ By some new estimates on the boundary related to the Navier-type slip boundary condition, the classical solution to the initial-boundary-value problem of this system exists globally in time provided the initial energy is suitably small even if the density has large oscillations and contains vacuum states. Futhermore, we also prove that the oscillation of the density will grow unboundedly in the long run wit…
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