1. Rotation-dominant three-scale limit of the Cauchy problem to the inviscid rotating stratified Boussinesq equations.
- Author
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Mu, Pengcheng and Wei, Zhengzhen
- Subjects
- *
BOUSSINESQ equations , *CAUCHY problem , *TRANSPORT equation , *STRATIFIED flow , *EULER equations , *ROSSBY number , *INVISCID flow , *FROUDE number - Abstract
In this paper, we investigate the rotation-dominant three-scale singular limit of the initial-value problem to the inviscid rotating stratified Boussinesq equations. We first prove a dispersive decay estimate for the linear propagator of that limit regime, which requires novel techniques involving an elaborate frequency cut-off since the phase function is degenerate on both horizontal and vertical directions in some areas. Using the dispersive decay estimate, we then investigate rigorously the rotation-dominant limit of local strong solutions to Boussinesq equations with ill-prepared initial data. The limiting system is shown to be the two-dimensional incompressible Euler equations coupled with a two-dimensional transport equation but in three spatial dimensions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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