21 citations · 44 across the 16 of their papers we have counts for
16 papers
Note on gradient estimate of heat kernel for Schrödinger operators
Shijun Zheng
Let be a Schrödinger operator on . We show that gradient estimates for the heat kernel of with upper Gaussian bounds imply polynomial decay for the kerne…
Damped nonlinear Schrödinger equation with Stark effect
Yi Hu, Yongki Lee, Shijun Zheng
We study the -critical damped NLS with a Stark potential. We prove that the threshold for global existence and finite time blowup of this equation is given by , where…
Shock formation in traffic flow models with nonlocal look ahead and behind flux
Yi Hu, Yongki Lee, Shijun Zheng
In this work, we study a Lighthill-Whitham-Richard (LWR) type traffic flow model with a non-local flux. We identify a threshold condition for shock formation for traffic flow model…
Universal Upper Bound on The Blowup Rate of Nonlinear Schrödinger Equation with Rotation
Yi Hu, Christopher Leonard, Shijun Zheng
In this paper, we prove a universal upper bound on the blowup rate of a focusing nonlinear Schrödinger equation with an angular momentum under a trapping harmonic potential, assumi…
Spectral multipliers for Schrödinger operators
Shijun Zheng
We prove a sharp Hörmander multiplier theorem for Schrödinger operators on . The result is obtained under certain condition on a weighted estimate…
Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation
Nyla Basharat, Hichem Hajaiej, Yi Hu +1
We consider the focusing NLS with an angular momentum and a harmonic potential, which models Bose-Einstein condensate under a rotating magnetic trap. We give a sharp condition on t…