English

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 B3,113B_{3,1}^{\frac{1}{3}}. 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