Blow up of solutions to 1-d Euler equations with time-dependent damping

DOI10.1016/j.jmaa.2016.04.075zbMath1342.35235OpenAlexW2346186211MaRDI QIDQ294092

Xinghong Pan

Publication date: 9 June 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.04.075

zbMATH Keywords

Euler equationsblow uptime-dependent damping

Mathematics Subject Classification ID

Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Blow-up in context of PDEs (35B44) Euler equations (35Q31)

Related Items (36)

Analytical solutions to the compressible Euler equations with time-dependent damping and free boundaries ⋮ Asymptotic behavior of solutions to bipolar Euler-Poisson equations with time-dependent damping ⋮ Classical solutions for 1D compressible Euler equations with over damping ⋮ Singularity formation for the 1D compressible Euler equations with variable damping coefficient ⋮ Vacuum and singularity formation for compressible Euler equations with time-dependent damping ⋮ Convergence rates to the Barenblatt solutions for the compressible Euler equations with time-dependent damping ⋮ Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques ⋮ The time asymptotic expansion for the compressible Euler equations with time-dependent damping ⋮ Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in \({\mathbb {R}}^n\): (II) Overdamping Case ⋮ Optimal convergence rate to nonlinear diffusion waves for bipolar Euler–Poisson equations with critical overdamping ⋮ Global solutions for the 1-D compressible Euler equations with time-dependent damping ⋮ Global existence of solutions to 1-d Euler equations with time-dependent damping ⋮ The best asymptotic profile of solutions to Euler equations with time‐dependent damping ⋮ Asymptotic stability of nonlinear diffusion waves for the bipolar quantum Euler–Poisson system with time‐dependent damping ⋮ Asymptotic behavior of solutions to the Euler-Korteweg equations with time-dependent damping ⋮ Blow-up for compressible Euler system with space-dependent damping in 1-D ⋮ Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping ⋮ Stability of smooth solutions for the compressible Euler equations with time-dependent damping and one-side physical vacuum ⋮ Optimal convergence rate to nonlinear diffusion waves for Euler equations with critical overdamping ⋮ Decay rates of solutions to Euler equations with time-dependent damping ⋮ Convergence to nonlinear diffusion waves for solutions of \(p\)-system with time-dependent damping ⋮ $L^1$-Convergence to Generalized Barenblatt Solution for Compressible Euler Equations with Time-Dependent Damping ⋮ Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping ⋮ Asymptotic Behavior of Solutions to Euler Equations with Time-Dependent Damping in Critical Case ⋮ Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping ⋮ Singularity formation for compressible Euler equations with time-dependent damping ⋮ The lifespan of classical solutions to the (damped) compressible Euler equations ⋮ Global and blow-up solutions for compressible Euler equations with time-dependent damping ⋮ Finite-time singularity formation for C¹ solutions to the compressible Euler equations with time-dependent damping ⋮ \(L^2\)-convergence to nonlinear diffusion waves for Euler equations with time-dependent damping ⋮ Large-time behavior of solutions to the bipolar quantum Euler-Poisson system with critical time-dependent over-damping ⋮ Optimal decay rates of the compressible Euler equations with time-dependent damping in \(\mathbb{R}^n\). I: Under-damping case ⋮ Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping ⋮ On finite-time blowup mechanism of irrotational compressible Euler equations with time-dependent damping ⋮ On global smooth solutions of the 3D spherically symmetric Euler equations with time-dependent damping and physical vacuum ⋮ Vacuum and singularity formation problem for compressible Euler equations with general pressure law and time-dependent damping

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