Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum

By Feimin Huang, Ronghua Pan. 2006

88 citations recorded by the source corpus.

Abstract The asymptotic behavior of solutions of the damped compressible Euler equations is conjectured to obey to the famous porous media equations (PMES). The previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic. In present paper, we prove that the L ∞ entropy weak solution with vacuum, obtained by the compensated compactness theory, converges strongly in L loc p ( 1 ⩽ p ∞ ) space to the unique similarity solution of the related PME, as time goes to infinity.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c49a5405a8e91e60936f118280bd9c02525cd246

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In Applied Mathematics

1. Zhen Wang
2. Feimin Huang
3. Ronghua Pan
4. V. Shelkovich
5. Juhi Jang
6. Nader Masmoudi
7. Meina Sun
8. Chun-fang Shen

In Computational Mechanics

1. Zhen Wang
2. Ronghua Pan
3. Feimin Huang

In Mathematical Physics

1. Zhen Wang
2. Ronghua Pan
3. Feimin Huang
4. Juhi Jang
5. Nader Masmoudi
6. Meina Sun
7. Chun-fang Shen

Citations in the corpus

• L1 Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping (2011, methodology): “Indeed, the only global weak solution with vacuum is constructed in L∞ space by using the method of compensated compactness; see Ding, Chen and Luo [10] for 1 < γ ≤ 3 and Huang and Pan [19] for 1 ≤ γ < 3.”