Zobrazeno 1 - 10
of 245
pro vyhledávání: '"Zhang, Qi S."'
Autor:
Qin, Lang, Zhang, Qi S.
In this paper, we remove the assumption on the gradient of the Ricci curvature in Hamilton's matrix Harnack estimate for the heat equation on all closed manifolds, answering a question which has been around since the 1990s. New ingredients include a
Externí odkaz:
http://arxiv.org/abs/2409.10379
Autor:
Zhang, Qi S.
Publikováno v:
Surveys in Geometric Analysis 2023, edited by Gang Tian, Qing Han, Zhenlei Zhang, Science Press, Beijing 2024, pp186-212
In this short survey paper, we first recall the log gradient estimates for the heat equation on manifolds by Li-Yau, R. Hamilton and later by Perelman in conjunction with the Ricci flow. Then we will discuss some of their applications and extensions
Externí odkaz:
http://arxiv.org/abs/2407.20719
Autor:
Zhang, Qi S.
Using a size condition of the sharp log Sobolev functional (log entropy) near infinity only, we prove a rigidity result for ancient Ricci flows without sign condition on the curvatures. The result is also related to the problem of identifying type II
Externí odkaz:
http://arxiv.org/abs/2406.17179
Autor:
Zhang, Qi S.
A forced solution $v$ of the axially symmetric Navier-Stokes equation in a finite cylinder $D$ with suitable boundary condition is constructed. The forcing term is in the super critical space $L^q_t L^1_x$ for all $q>1$. The velocity is in the energy
Externí odkaz:
http://arxiv.org/abs/2311.12306
Autor:
Li, Xiaolong, Zhang, Qi S.
In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply such estimates to establish the monotonicity of parabolic fr
Externí odkaz:
http://arxiv.org/abs/2306.10143
Autor:
Zhang, Qi S.
Let $v$ be a solution of the axially symmetric Euler equations (ASE) in a finite cylinder in $\mathbb{R}^3$. We show that suitable blow-up limits of possible velocity singularity and most self similar vorticity singularity near maximal points off the
Externí odkaz:
http://arxiv.org/abs/2306.09515
Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in a $C^2(\ov
Externí odkaz:
http://arxiv.org/abs/2207.08861
Autor:
Zhang, Qi S.
Let $(\M^n, g)$ be a $n$ dimensional, complete ( compact or noncompact) Riemannian manifold whose Ricci curvature is bounded from below by a constant $-K \le 0$. Let $u$ be a positive solution of the heat equation on $\M^n \times (0, \infty)$. The we
Externí odkaz:
http://arxiv.org/abs/2110.08933
The existence of smooth but nowhere analytic functions is well-known (du Bois-Reymond, Math. Ann., 21(1):109-117, 1883). However, smooth solutions to the heat equation are usually analytic in the space variable. It is also well-known (Kowalevsky, Cre
Externí odkaz:
http://arxiv.org/abs/2109.07014