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Perturbational blowup solutions to the compressible Euler equations with damping
1Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories Hong Kong.
Springerplus
|March 31, 2016
Summary
Researchers constructed exact solutions for the one-dimensional isentropic compressible Euler equations with damping. These solutions reveal both blowup and global existence behaviors, aiding fluid dynamics research.
Area of Science:
- Fluid Dynamics
- Partial Differential Equations
- Mathematical Physics
Background:
- The isentropic compressible Euler system with damping is fundamental in fluid dynamics.
- General closed-form solutions are unavailable for arbitrary initial value problems.
- Exact solutions provide crucial insights into system behavior.
Purpose of the Study:
- To construct novel exact solutions for the 1D isentropic compressible Euler equations with damping.
- To analyze the properties and classification of these solutions.
- To provide tools for validating numerical methods.
Main Methods:
- Perturbational method applied to derive exact solutions.
- Analysis of the governing ordinary differential equation.
- Investigation of solution behavior based on chosen parameters.
Main Results:
- Two families of exact solutions were successfully constructed.
- Solutions exhibit both finite-time blowup and global existence depending on parameters.
- Identified essential singularities in blowup cases, which are non-removable.
Conclusions:
- The derived exact solutions are valuable for understanding fluid dynamics.
- These solutions can serve as benchmarks for numerical methods like finite difference, finite element, and finite volume methods.
- Facilitates accurate simulation of fluid behavior in various applications.
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