The Lifespan of Classical Solutions to the (Damped) Compressible Euler Equations

Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach

“…Note that if p(ρ) = Cρ q , ρ ≥ 0, C > 0, q ≥ 1, then, the fluid is called isentropic and isothermal when q > 1 and q = 1, respectively. For other possibilities of the pressure function, readers may refer to [5] and the references therein. Cauchy problem with bounded measurable initial data for (1.1):…”

“…For Euler equations with damping, the global existence of solutions can be found in [24], [27], [30] and the references therein. In [5], a class of conditions for non-existence of global classical solutions is established for the initial-boundary value problem of a three-dimensional compressible Euler equations with (or without) time-dependent damping. We mention also the works [15], [26] and [28].…”