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Analytical solutions and asymptotic profiles of vacuum free boundary for the compressible Euler equations with time-dependent damping

Analytical solutions and asymptotic profiles of vacuum free boundary for the compressible Euler equations with time-dependent damping

Abstract We constructed a class of analytical, rotationaland self-similar solutions to the isentropic compressible Euler equations with time-dependent damping $\frac{\mu}{\left( 1+t\right) ^{\lambda}}%\rho\mathbf{u}$ ($\mu\geq0$, $\lambda\in\mathbb{R}$) and vacuum free boundary in cylindrical coordinates. These solutions capture the precise physical vacuum behavior that the sound speed is $C^{1/2}$-H\"older continuous across the boundary and …