Digital Object Identifier (DOI) 10.1007/s00205-004-0349-y Convergence to the Barenblatt Solution for the Compressible Euler Equations with Damping and Vacuum
Digital Object Identifier (DOI) 10.1007/s00205-004-0349-y Convergence to the Barenblatt Solution for the Compressible Euler Equations with Damping and Vacuum
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DOI：
10.1007/s00205-004-0349-y
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发表时间：
2005-02
影响因子：
2.5
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中科院分区：
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研究了初始质量有限时多孔介质中可压缩等熵流的渐近行为。模型系统为带摩擦阻尼的可压缩欧拉方程。当Ast→∞时，密度服从多孔介质方程，动量服从达西定律。在本文中，我们给出了一个明确的答案，这个猜想没有任何假设的小或规则的初始数据。本文证明了有限初始质量阻尼Euler方程Cauchy问题的任意L ∞弱熵解都强收敛于L p，且具有衰减率，与多孔介质方程的Barenblatt剖面相匹配.密度函数趋向于多孔介质方程的巴伦布拉特解，而动量由达西定律描述。
We study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. Ast→∞, the density is conjectured to obey the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. In this paper, we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data. We prove that anyL∞weak entropy solution to the Cauchy problem of damped Euler equations with finite initial mass converges, strongly inLpwith decay rates, to matching Barenblatt’s profile of the porous medium equation. The density function tends to the Barenblatt’s solution of the porous medium equation while the momentum is described by Darcy’s law.