论文标题
Hodge-Neumann Heat内核的构建，本地伯恩斯坦估计以及Onsager在流体动力学中的猜想
Construction of the Hodge-Neumann heat kernel, local Bernstein estimates, and Onsager's conjecture in fluid dynamics
论文作者
论文摘要
最近，在Arxiv：1907.05360 [Math.ap]中，我们介绍了可加热电流的理论，并证明了Sagager对带边界的Riemannian歧管的猜想，其中弱解决方案具有$ b_ {3,1}^{\ frac {\ frac {1}} {3} {3} {3}}} $ Spatial jullistial $ Spatial patial patial patial patial。在此续集中，通过应用几何微局部分析的技术来构建Hodge-Neumann Heat内核，我们获得了异位衰减和伯恩斯坦当地的估计，然后使用它们将结果扩展到Besov space $ \ wideHat {B} $ \ wideHat {b} _ {3，c（\ sathbb {n}）}}^{1/3} $来自arxiv：1310.7947 [nath.ap]和空间$ \ space $ \ useverline {b} _ {b} _ {3，{3，\ text {vmo}}}}}^{1/3} $1/10-19020020。已知的功能空间，其中Onsager的猜想在平坦的背景上保持。
Most recently, in arXiv:1907.05360 [math.AP], we introduced the theory of heatable currents and proved Onsager's conjecture on Riemannian manifolds with boundary, where the weak solution has $B_{3,1}^{\frac{1}{3}}$ spatial regularity. In this sequel, by applying techniques from geometric microlocal analysis to construct the Hodge-Neumann heat kernel, we obtain off-diagonal decay and local Bernstein estimates, and then use them to extend the result to the Besov space $\widehat{B}_{3,V}^{\frac{1}{3}}$, which generalizes both the space $\widehat{B}_{3,c(\mathbb{N})}^{1/3}$ from arXiv:1310.7947 [math.AP] and the space $\underline{B}_{3,\text{VMO}}^{1/3}$ from arXiv:1902.07120 [math.AP] -- the best known function space where Onsager's conjecture holds on flat backgrounds.
