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arXiv · 2610.40334

Stationary Structures of the Boussinesq equations

Marc Nualart·Jaemin Park·Javier Peñafiel-Tomás
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Abstract

We investigate the steady configurations supported by the inviscid two-dimensional Boussinesq equations in the periodic channel. We show steady laminar velocity fields (closed non-contractible fluid trajectories) coupled to non-decreasing density stratifications are necessarily stratified shear flows. The direction of density monotonicity along level sets is in fact fundamental: in striking contrast with the Euler equations, we exhibit laminar non-stagnant non-shear stationary solutions in the periodic channel. We also provide distinct flexibility and rigidity results (laminar persistence or appearance of islands for nearby non-shear solutions) close to stratified shear flows according to their stagnation points. As a by-product of our analysis, we establish a uniform Crandall-Rabinowitz bifurcation theorem that might be of independent interest.

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Marc Nualart, Jaemin Park, Javier Peñafiel-Tomás. 2026-10-29. Stationary Structures of the Boussinesq equations. https://arxiv.org/abs/2610.40334

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