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- Title
On Stability Estimates for the Inviscid Boussinesq Equations.
- Authors
Zillinger, Christian
- Abstract
We consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow v = (y , 0) and a stratified temperature θ = α y with α > 1 4 . We show that for any ϵ > 0 there exist non-trivial explicit solutions, which are initially perturbations of size ϵ , and grow to size 1 on a time scale ϵ - 2 . Moreover, the (simplified) linearized problem around these non-trivial states exhibits improved upper bounds on the possible size of norm inflation for frequencies larger and smaller than ϵ - 4 .
- Publication
Journal of Nonlinear Science, 2023, Vol 33, Issue 6, p1
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-023-09958-2