Professor Zhang has two main research directions in applied mathematics. In the first direction, he studies the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of n-dimensional incompressible fluid dynamics equations, including the magnetohydrodynamics equations, the Navier-Stokes equations, the two-dimensional dissipative quasi-geostrophic equation, and many other similar equations.

In the second direction, he studies the existence and stability of traveling pulse solutions of nonlinear singularly perturbed systems of integral differential equations arising from synaptically coupled neuronal networks (and the existence and stability of traveling wave fronts of nonlinear scalar integral differential equations).

Additionally, Professor Zhang has a minor research direction. He studies explicit representations of bounded smooth traveling wave solutions of five kinds of nonlinear evolution equations with strong physical backgrounds.