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Wave breaking and shock waves for a periodic shallow water equation
1Institute for Applied Mathematics, Leibniz University of Hanover, 30167 Hanover, Germany. escher@ifam.uni-hannover.de
Summary
This study analyzes a periodic shallow water equation, detailing conditions for wave breaking in strong solutions. It also introduces global weak solutions representing periodic shock waves.
Area of Science:
- Fluid dynamics
- Nonlinear partial differential equations
Background:
- The periodic shallow water equation is a recent model.
- Understanding wave breaking and shock wave formation is crucial.
Purpose of the Study:
- Investigate the blow-up scenario of strong solutions.
- Identify conditions leading to wave breaking.
- Characterize global weak solutions as periodic shock waves.
Main Methods:
- Analysis of strong solutions for blow-up criteria.
- Construction and analysis of global weak solutions.
Main Results:
- Established conditions ensuring wave breaking for strong solutions.
- Presented a family of global weak solutions.
- Characterized these weak solutions as periodic shock waves.
Conclusions:
- The study provides a comprehensive analysis of the periodic shallow water equation.
- Identified mechanisms for wave breaking and the existence of periodic shock waves.
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