Convergence to the Barenblatt Solution for the Compressible Euler Equations with Damping and Vacuum

By Feimin Huang, Pierangelo Marcati, Ronghua Pan. 2005

163 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/112e4265260e331a7866294c97766fbd8a94c707

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In Applied Mathematics

1. Juhi Jang
2. Nader Masmoudi
3. Huihui Zeng
4. Tao Luo
5. Zhen Wang
6. Feimin Huang
7. Ronghua Pan
8. Hongyun Peng

In Mathematical Physics

1. Juhi Jang
2. Nader Masmoudi
3. Zhen Wang
4. Huihui Zeng
5. Tao Luo
6. Ronghua Pan
7. Feimin Huang
8. Hongyun Peng

Citations in the corpus

• GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION (2010, result): “In this barotropic case, there are several existing theoretical results [28], [21], [22] justifying the formal analysis above.”
• Well‐posedness for compressible Euler equations with physical vacuum singularity (2008, methodology): “This conjecture was established in [4] in the entropy solution framework where the method of compensated compactness yields a global weak solution in L∞.”
• Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, methodology): “This conjecture was established by Huang, Marcati and Pan [26] in the framework of the entropy solution where the method of compensated compactness yields a global weak solution in L∞.”
• Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis (2021, methodology): “[17, 21, 22, 28, 32, 33, 36–39, 46] without vacuum and [7, 18, 29, 40] with vacuum), as well as the Euler-Poisson system of semiconductors [14], bipolar Euler-Maxwell equation [8], Timoshenko system [20] and the radiating gas model [27].”
• L1 Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping (2011, methodology): “‐ Question 1: Is it possible to remove assumption (1.5)? Assumption (1.5 )i s essential in the proof of [ 21 ].”
• Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping (2014, methodology): “It should be pointed that the L-convergence of L-weak solutions for the Cauchy problem of the one-dimensional compressible Euler equations with damping to Barenblatt solutions of the porous media equations was given in [9] with p = 2 if 1 < γ ≤ 2 and p = γ if γ > 2 and in [10] with p = 1, respective”