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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Well-Posedness Properties for a Stochastic Rotating Shallow Water Model
1Department of Mathematics, Imperial College London, London, UK.
Journal of Dynamics and Differential Equations
|November 18, 2024
Summary
This study investigates the stochastic rotating shallow water system, demonstrating a unique maximal solution exists and is continuous with initial conditions. The research confirms a strictly positive interval of existence and global solutions with positive probability.
Area of Science:
- Fluid Dynamics
- Stochastic Partial Differential Equations
- Mathematical Physics
Background:
- The stochastic rotating shallow water system is a crucial model in geophysical fluid dynamics.
- Previous work established an inviscid version of this model.
- The incorporation of noise is based on the Stochastic Advection by Lie Transport theory.
Purpose of the Study:
- To analyze the well-posedness properties of the stochastic rotating shallow water system.
- To investigate the existence and uniqueness of solutions under specific noise conditions.
- To determine the nature of the solution's existence interval and global behavior.
Main Methods:
- The study employs mathematical analysis to examine the system's behavior.
- Well-posedness is investigated for a system perturbed by noise modulated by a non-Lipschitz function.
- Techniques are used to establish the existence and continuity of solutions.
Main Results:
- A unique maximal solution is shown to exist for the stochastic rotating shallow water system.
- The solution demonstrates continuous dependence on the initial condition.
- The interval of existence is proven to be strictly positive, with global solutions occurring with positive probability.
Conclusions:
- The stochastic rotating shallow water system exhibits well-posedness properties.
- The findings confirm the existence of a unique, continuous, and globally existing solution under specific stochastic perturbations.
- This research contributes to the understanding of complex fluid dynamics models with stochastic influences.
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