BOUSSINESQ EQUATIONS IN THIN SPHERICAL DOMAINS

The Euler Equations on Thin Domains

For the Euler equations in a thin domain Qε = Ω×(0, ε), Ω a rectangle in R, with initial data in (W (Qε)), q > 3, bounded uniformly in ε, the classical solution is shown to exist on a time interval (0, T (ε)), where T ( ) → +∞ as → 0. We compare this solution with that of a system of limiting equations on Ω.

Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

Global Regularity of the Two-dimensional Boussinesq Equations without Diffusivity in Bounded Domains

We address the well-posedness for the two-dimensional Boussinesq equations with zero diffusivity in bounded domains. We prove global in time regularity for rough initial data: both the initial velocity and temperature have ǫ fractional derivatives in L for some q > 2 and ǫ > 0 arbitrarily small.

The 2D Incompressible Boussinesq Equations

Effective action in spherical domains

The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes ζ–functions and it is shown how these may be evaluated. Numerical values are shown. An analytical, heat-kernel derivation of the Cesàro-Fedorov formula for the number of symmetry planes of a regular solid is also presented. 1 1. Introduction. ...