18 citations · 27 across the 8 of their papers we have counts for
8 papers
Exactly self-similar blow-up of the generalized De Gregorio equation
Fan Zheng
We study exactly self-similar blow-up profiles fot the generalized De Gregorio model for the three-dimensional Euler equation: We show that for…
Long-term regularity of 2D gravity water waves
Fan Zheng
The two dimensional gravity water wave problem concerns the motion of an incompressible fluid occupying half the 2D space and flowing under its own gravity. In this paper we study…
Stability of traveling waves for the Burgers-Hilbert equation
Ángel Castro, Diego Córdoba, Fan Zheng
We consider smooth solutions of the Burgers-Hilbert equation that are a small perturbation from a global periodic traveling wave with small amplitude . We use a modified ene…
The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation
Ángel Castro, Diego Córdoba, Fan Zheng
We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation from a radial stationary solution . We use a modified en…
Long-term regularity of 3D gravity water waves
Fan Zheng
We study a fundamental model in fluid mechanics--the 3D gravity water wave equation, in which an incompressible fluid occupying half the 3D space flows under its own gravity. In th…
Long-term regularity of the periodic Euler--Poisson system for electrons in 2D
Fan Zheng
We study a basic plasma physics model--the one-fluid Euler--Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In t…
Locating the first nodal set in higher dimensions
Fan Zheng
This paper estimates the location and the width of the nodal set of the first Neumann eigenfunctions on a smooth convex domain , whose length is normalized to…
Gauss Sphere Problem with Polynomials
Fan Zheng
This paper provides an estimate of the sum of a homogeneous polynomial of degree and mean zero over the lattice points inside a sphere of radius . It is proved that $$ \…