Existence of global smooth solutions for non-isentropic compressible Euler equations with time-dependent damping
Abstract
Abstract In this paper, we consider the non-isentropic compressible Euler equations with time-dependent damping − α ( t ) u in one space dimension v t − u x = 0 , u t + p ( v , s ) x = − α ( t ) u , s t = 0 . $$\begin{cases}_{t}-{u}_{x}=0,\hfill \\ {u}_{t}+p{\left(v,s\right)}_{x}=-\alpha \left(t\right)u,\hfill \\ {s}_{t}=0.\hfill \end{cases}$$ Under some conditions on the initial data and the entropy function, we prove some existence theorems of global smooth solutions for the Cauchy problem. At present, there seems to be no research on this kind of problem.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Demonstratio Mathematica
- Publisher
- Walter de Gruyter GmbH
- Volume
- 59
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN