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

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.

arXiv commentUpdates: simplified some interpolation steps, fixed some typos, added some references by Huy's suggestions

References in corpus (7)

• Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit
• Onsager's conjecture and anomalous dissipation on domains with boundary
• Paley-Littlewood decomposition for sectorial operators and interpolation spaces
• Onsager's conjecture on the energy conservation for solutions of Euler equations in bounded domains
• Weighted Besov and Triebel--Lizorkin spaces associated to operators
• Tempered currents and the cohomology of the remote fiber of a real polynomial map
• Elliptic problems and holomorphic functions in Banach spaces