Shiliang Zhao

activity

20192026

most citedLocal well-posedness of semilinear space-time fractional Schrödinger equation

1 citations · 3 across the 8 of their papers we have counts for

collaborators

8 papers

math.FA2026

Extension of Sobolev functions on balls in infinite dimensions

Zhouzhe Wang, Xu Zhang, Shiliang Zhao

We prove the existence of a bounded Sobolev extension operator $E : W^{p, 1} (B, P) \to W^{p, 1} (ℓ^{2}, P)$ using a completely new method, where $B\s…

math.FA2026

Sobolev spaces in infinite dimensions

Zhouzhe Wang, Jiayang Yu, Xu Zhang +2

The classical theory of Sobolev spaces in finite dimensions is well established. Because infinite-dimensional spaces possess inherent analytical and topological complexities, devel…

math.CA2020★ 1 cited

Uniform Complex Time Heat Kernel Estimates Without Gaussian Bounds

Shiliang Zhao, Quan Zheng

In this paper, first we consider the uniform complex time heat kernel estimates of $e^{- z (- Δ)^{\frac{α}{2}}}$ for $α > 0, z \in C^{+}$ . When $\frac{α}{2}$ is not an integer, genera…

math.DG2020

Conformal Perturbation of Heat Kernels with applications

Shiliang Zhao

Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n \geq 2$ . Consider the conformal perturbation $g ~ = h g$ where $h$ is a smooth bounded positive function on $M$ .…

math.AP2019

Global well-posedness of cubic fractional Schrödinger equations in one dimension

Huali Zhang, Shiliang Zhao

In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schrödinger equations in o…

math.AP2019

Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature

Huali Zhang, Shiliang Zhao

In this paper, the well-posedness of Cauchy's problem of fractional Schrödinger equations with a power type nonlinearity on $n$ -dimensional manifolds with nonnegative Ricci curvatu…

math.AP2019★ 1 cited

Dispersive estimates for time and space fractional Schrödinger equations

Xiaoyan Su, Shiliang Zhao, Miao Li

In this paper, we consider the Cauchy problem for the fractional Schrödinger equation $i D_{t}^{α} u + (- Δ)^{\frac{β}{2}} u = 0$ with $0 < α < 1$ , $β > 0$ . We establish the dispersive estimates…

math.AP2019★ 1 cited

Local well-posedness of semilinear space-time fractional Schrödinger equation

Xiaoyan Su, Shiliang Zhao, Miao Li

The semilinear space-time fractional Schrödinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$ -functions in order to t…