2 1 M ar 2 00 7 Existence and asymptotic behavior of C 1 solutions to the multidimensional compressible Euler equations with damping ∗
نویسندگان
چکیده
In this paper, the existence and asymptotic behavior of C solutions to the multidimensional compressible Euler equations with damping on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve the well-posedness results of Sideris-ThomasesWang (Comm.P.D.E. 28 (2003) 953). The global existence lies on a crucial a-priori estimate which is proved by the spectral localization method. The main analytic tools are the Littlewood-Paley decomposition and Bony’s para-product formula. MSC: 35L65; 76N15
منابع مشابه
Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition
The asymptotic behavior as well as the global existence of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas P ρ P0ρ , time asymptotically, it has been proved by Pan and Zhao 2009 that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy’s law. In this paper...
متن کاملConvergence Rate for Compressible Euler Equations with Damping and Vacuum
We study the asymptotic behavior of L∞ weak-entropy solutions to the compressible Euler equations with damping and vacuum. Previous works on this topic are mainly concerned with the case away from the vacuum and small initial data. In the present paper, we prove that the entropy-weak solution strongly converges to the similarity solution of the porous media equations in L(R) (2 p < ∞) with deca...
متن کاملLong Time Behavior of Solutions to the 3d Compressible Euler Equations with Damping
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum nor...
متن کاملM ar 2 00 8 Well - posedness of the IBVP for 2 - D Euler Equations with Damping ∗
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-intime existence of classical solution to the initial-boundary value problem by the method of energy estimates. keywords: Euler equation; initial-boundary value problem; well-posedness. MSC(2000): 35A05; 35L45.
متن کاملAsymptotics Toward Rarefaction Waves and Vacuum for 1-d Compressible Navier-Stokes Equations
In this work we study time asymptotic behavior of solutions of 1-d Compressible Navier-Stokes equations toward solutions of Euler equations that consist of two rarefaction waves separated by a vacuum region. The analysis relies on various energy estimates. 0.1 Summary and the main result Time asymptotic toward rarefaction waves for Compressible Navier-Stokes equations for barotropic fluids was ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007