Hodge-theoretic analysis on manifolds with boundary, heatable currents, and Onsager's conjecture in fluid dynamics
Analysis of PDEs
2019-07-16 v2 Classical Analysis and ODEs
Functional Analysis
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 . We also introduce heatable currents as the natural analogue to tempered distributions and justify their importance in Hodge theory.
Keywords
Cite
@article{arxiv.1907.05360,
title = {Hodge-theoretic analysis on manifolds with boundary, heatable currents, and Onsager's conjecture in fluid dynamics},
author = {Khang Manh Huynh},
journal= {arXiv preprint arXiv:1907.05360},
year = {2019}
}
Comments
Updates: simplified some interpolation steps, fixed some typos, added some references by Huy's suggestions