Liouville type theorem for the stationary equations of magneto-hydrodynamics

Simon Schulz

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arXiv · 1710.07079

Liouville type theorem for the stationary equations of magneto-hydrodynamics

Simon Schulz

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Abstract

We show that any smooth solution $(\mathbf{u},\mathbf{H})$ to the stationary equations of magneto-hydrodynamics (MHD) belonging to both spaces $L^6 (\mathbb{R}^3)$ and $BMO^{-1}(\mathbb{R}^3)$ must be identically zero. This is an extension of previous results, all of which systematically required stronger integrability and the additional assumption $\nabla \mathbf{u}, \nabla \mathbf{H} \in L^2 (\mathbb{R}^3) $, i.e., finite Dirichlet integral.

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Simon Schulz. 2017-10-19. Liouville type theorem for the stationary equations of magneto-hydrodynamics. https://arxiv.org/abs/1710.07079

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