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- Title
Analytical solutions to the compressible Euler equations with cylindrical symmetry and free boundary.
- Authors
Dong, Jianwei; Wang, Longquan; Chen, Hao
- Abstract
In this paper, we study the analytical solutions to the compressible Euler equations with cylindrical symmetry and free boundary. We assume that the free boundary is moving in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. By using some ansatzs, we reduce the original partial differential equations into an ordinary differential equation about the free boundary. We prove that the free boundary grows linearly in time by constructing some new physical functionals. Furthermore, the analytical solutions to the compressible Euler equations with time-dependent damping are also considered and the spreading rate of the free boundary is investigated according to the various sizes of the damping coefficients.
- Subjects
EULER equations; ORDINARY differential equations; ANALYTICAL solutions; PARTIAL differential equations; DIFFERENTIAL equations; ANGULAR velocity
- Publication
Journal of Hyperbolic Differential Equations, 2024, Vol 21, Issue 1, p143
- ISSN
0219-8916
- Publication type
Article
- DOI
10.1142/S021989162450005X