Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping

By T. Sideris, B. Thomases, Dehua Wang. 2003

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On the global existence and blowup of smooth solutions of 3-D compressible Euler equations with time-depending damping (2015, background): “pressible Euler equations with time-depending damping where ρ˜0,u˜0 ∈ C∞ 0 (R3), supp ˜ρ0,supp ˜ρ0 ⊆ B(0,M) ≡ {x: |x| ≤ M}, and ρ(0,·) >0. Motivated by the treatment of the special case of λ= 0 in [19], we introduce the functions H(t) ≡ Z R3 x·(ρu)(t,x)dx, L(t) ≡ Z R3 (ρ(t,x) −ρ¯)dx, α(t) ≡ (t+M)”
The strong relaxation limit of the multidimensional isothermal Euler equations (2006, background): “We refer the reader to [8] for the existence of global smooth solutions in the isentropic case.”
Decay estimates for hyperbolic balance laws (2009, methodology): “In addition, a quite different approach was used in [13] to show the global existence for a specific model – three-dimensional compressible Euler equations with damping.”
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems (2011, background): “Before the papers [36] and [13], which are of general breadth, there were a few papers restricted to specific examples, such as [18,19,31].”