Analytical solutions to the compressible Euler equations with cylindrical symmetry and free boundary

被引：2

作者：

Dong, Jianwei ^{[1
]}

Wang, Longquan ^{[2
]}

Chen, Hao ^{[1
]}

机构：

[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450015, Peoples R China

[2] China Univ Min & Technol, Sch Math, Xuzhou 221116, Peoples R China

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2024年 / 21卷 / 01期

关键词：

Compressible Euler equations; free boundary; cylindrical symmetry; analytical solutions; DENSITY-DEPENDENT VISCOSITY; STOKES-POISSON EQUATIONS; GLOBAL EXISTENCE; PHYSICAL VACUUM; SMOOTH SOLUTIONS; WELL-POSEDNESS; BLOWUP SOLUTIONS; NONLINEAR DIFFUSION; ASYMPTOTIC-BEHAVIOR; CONVERGENCE;

D O I：

10.1142/S021989162450005X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：143 / 163

页数：21

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