Theoretical analysis demonstrates local well-posedness in three-dimensional damped wave Boussinesq systems, indicating validity of the hydrostatic approximation under Gevrey regularity.
We study the hydrostatic approximation for the three-dimensional Boussinesq equations of damped wave type. This is a mixed degenerate system coupled with parabolic and hyperbolic equations. Compared with the purely hyperbolic hydrostatic Navier–Stokes equations, the parabolic equation for temperature will lead to an extra loss of derivatives. In the setting of Gevrey space with index [Formula: see text], we prove the local well-posedness and the corresponding hydrostatic limit for the three-dimensional Boussinesq equations of damped wave type.
No takes yet. Share an insight, caveat, or question.
Li et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: