Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer
نویسندگان
چکیده
منابع مشابه
On the isentropic compressible Navier-Stokes equation
In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...
متن کاملSpectral properties of the linearized compressible Navier-Stokes equation around time-periodic parallel flow
The linearized problem around a time-periodic parallel flow of the compressible Navier-Stokes equation in an infinite layer is investigated. By using the Floquet theory, spectral properties of the evolution operator associated with the linearized problem are studied in detail. The Floquet representation of low frequency part of the evolution operator, which plays an important role in the study ...
متن کاملInfinite Dimensional Dynamical Systems and the Navier-Stokes Equation
In this set of lectures I will describe how one can use ideas of dynamical systems theory to give a quite complete picture of the long time asymptotics of solutions of the two-dimensional Navier-Stokes equation. I will discuss the existence and properties of invariant manifolds for dynamical systems defined on Banach spaces and review the theory of Lyapunov functions, again concentrating on the...
متن کاملControllability and Stabilizability of the Linearized Compressible Navier-Stokes System in One Dimension
In this paper we consider the one-dimensional compressible Navier–Stokes system linearized about a constant steady state (Q0, 0) with Q0 > 0. We study the controllability and stabilizability of this linearized system. We establish that the linearized system is null controllable for regular initial data by an interior control acting everywhere in the velocity equation. We prove that this result ...
متن کاملRemark on the Rate of Decay of Solutions to Linearized Compressible Navier-stokes Equations
ρ0 and v0 are given initial data; α and γ are positive constants and β a nonnegative constant. Concerning the decay property, asymptotically, the solution decomposed into sum of two parts under the influence of a hyperbolic aspect and a parabolic aspect. One of which dominates in Lp for 2 p ∞, the other 1 p < 2. For p 2, the time asymptotic behavior of solutions is similar to the solution of pu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Funkcialaj Ekvacioj
سال: 2007
ISSN: 0532-8721
DOI: 10.1619/fesi.50.287