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二维等熵可压欧拉方程古典解的存在性(英文)论文

导读:本论文是一篇关于二维等熵可压欧拉方程古典解的存在性(英文)的优秀论文范文,对正在写有关于二维等熵可压欧拉方程古典解的存在性(英文)论文的写作者有一定的参考和指导作用,《二维等熵可压欧拉方程古典解的存在性(英文)论文》论文片段: the initial density is nonnegative. For the blow-up criterion problem, refer for instance to  and references therein.  For incompressible case, Schaefferand McGrathresearched the Euler equations in R2. In , Temam obtained the local existence of classical solution of Euler equations.  Motivated 

二维等熵可压欧拉方程古典解的存在性(英文)论文WORD版下载 英语论文范文 :
AbstractIn this paper, the authors study the local existence of classical solution of the 2D isentropic compressible Euler equation, by using the iterative approach, the local existence and uniqueness is obtained, and also proved that the solution blow up infinite time, that is, there is no global classical solution for compressible Euler equation.
  Key wordsIsentropic compressible Euler equations; Local existence; Blow-up criterion
  CLC numberO 175Document codeA
  1Introduction
  In this paper, we consider the 2D isentropic compressible Euler equations as follow:
  The Euler equations is used to describe the perfectfluids which corresponds to the particular case of Navier-Stokes equations. The Navier-Stokes equations for isentropic compressibleflow in two dimension can be express in the form
  rnal force, the viscosity coefficientsλandμsatisfyλ> 0,≥
  Many results concerning the local existence of equations (3) can be found in [1-4] whenρ0> 0. There are also some local existence results in [5-7] when the initial density is nonnegative. For the blow-up criterion problem, refer for instance to [8-11] and references therein.
  For incompressible case, Schaeffer[12]and McGrath[13]researched the Euler equations in R2. In [14], Temam obtained the local existence of classical solution of Euler equations.
  Motivated by [12,14], we consider the local existence of classical solution of the 2D isentropic compressible Euler equation. Our main results are formulated as following theorems:
  Theorem 1Assume that (ρ0,u0)∈Hs(R2)×Hs(R2) for some s > 2. Then there exists a unique local classical solution (ρ,u)∈C([0,T);Hs(R2)×Hs(R2)) to the Cauchy problem (1)-(2), for some T = T(∥ρ0∥Hs(R2),∥u0∥Hs(R2)).
  The rest of the paper is organized as follows: In Section 2, we state some elementary facts and

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1Introduction  In this paper, we consider the 2D isentropic compressible Euler equations as follow:  The Euler equations is used to describe the perfectfluids which corresponds to the particular case of Navier-Stokes equations. The Navier-Stokes equations for isentropic compressibleflow in two dWWw.YingyuLunwen.com 英语论文网整理提供

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