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arXiv · 1907.05360

Hodge-theoretic analysis on manifolds with boundary, heatable currents, and Onsager's conjecture in fluid dynamics

Khang Manh Huynh
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Abstract

We use Hodge theory and functional analysis to develop a clean approach to heat flows and Onsager's conjecture on Riemannian manifolds with boundary, where the weak solution lies in the trace-critical Besov space $B_{3,1}^{\frac{1}{3}}$. We also introduce heatable currents as the natural analogue to tempered distributions and justify their importance in Hodge theory.

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Khang Manh Huynh. 2019-07-11. Hodge-theoretic analysis on manifolds with boundary, heatable currents, and Onsager's conjecture in fluid dynamics. https://arxiv.org/abs/1907.05360

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