Abstract
AbstractWe consider a class of steady solutions of the semi-geostrophic equations on $${\mathbb {R}}^3$$
R
3
and derive the linearised dynamics around those solutions. The linear PDE which governs perturbations around those steady states is a transport equation featuring a pseudo-differential operator of order 0. We study well-posedness of this equation in $$L^2({\mathbb {R}}^3,{\mathbb {R}}^3)$$
L
2
(
R
3
,
R
3
)
introducing a representation formula for the solutions, and extend the result to the space of tempered distributions on $${\mathbb {R}}^{3}$$
R
3
. We investigate stability of the steady solutions of the semi-geostrophic equations by looking at plane wave solutions of the associated linearised problem, and discuss differences in the case of the quasi-geostrophic equations.
Funder
Maxwell Institute Graduate School in Analysis and its Applications
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
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