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arXiv · 2608.19035

A Ginzburg-Landau approximation theorem for quasilinear pattern-forming systems in uniformly local Sobolev spaces

Théo Belin·Guido Schneider
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Abstract

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear or fully nonlinear pattern-forming systems close to the first instability. We present an approximation theory in uniform local Sobolev spaces which is applied to a quasilinear Swift-Hohenberg model, to a quasilinear version of B\'enard's problem with velocity dependent viscosity, and to abstract quasilinear reaction-diffusion-advection systems.

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Théo Belin, Guido Schneider. 2026-08-19. A Ginzburg-Landau approximation theorem for quasilinear pattern-forming systems in uniformly local Sobolev spaces. https://arxiv.org/abs/2608.19035

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