Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

TL;DR

This paper proves the existence of heteroclinic solutions in a 6D system derived from fluid dynamics, providing insights into domain walls between orthogonal convective rolls using variational methods.

Contribution

It introduces a variational approach to establish heteroclinic orbits in a high-dimensional system related to convection patterns, linking mathematical theory with fluid dynamics phenomena.

Findings

Existence of heteroclinic solutions proven mathematically.

Constructed solutions approximate domain walls between orthogonal rolls.

Provides a first-order approximation for complex fluid flow structures.

Abstract

Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability threshold. The constructed heteroclinic solutions provide first order approximations for domain walls between two orthogonal convective rolls.