arXiv subjects

Chengfei Ai

Publications and source records attributed to Chengfei Ai.

4 recordsLinked to original sources

arXiv2026

Global solutions of the 2D inhomogeneous incompressible viscoelastic system

In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for the corresponding problem on $\mathbb{R}^{3}$ cannot be directly applied to the two-dimensional case. To overcome the main difficulties, we first transform the original system into a suitable dissipative system by introducing an effective tensor. Then we develop a new fractional time-weighted energy framework, combined with elegant commutator and bilinear estimates, to prove the global existence of strong solutions without the help of the common ``div-curl" structure on the viscoelastic system.

math.AP↗

arXiv2026

Global solutions of the 3D inhomogeneous incompressible viscoelastic system without structure assumptions

In this paper, we prove the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system without any additional structure assumptions on $\mathbb{R}^{3}$. Unlike the time weighted energy method presented by Ai and Wang (Nonlinear Anal. 254 (2025), 113747.), by replacing $H^{-1}$ conditions with certain $L^{1}$ conditions on initial data, we need to develop some new transformation techniques for the system (1.1) and make use of elegant spectral analysis method to capture an enhanced time-decay rate of the velocity field $u$, which is essential to establish the uniform bounds of the density and deformation tensor.

math.AP↗

arXiv2024

Global solutions of the 3D incompressible inhomogeneous viscoelastic system

In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We do not assume the "initial state" assumption and the "div-curl" structure inspired by the works [59,61]. It is a key to transform the original system into a suitable dissipative system by introducing a new effective tensor, which is useful to establish a series of energy estimates with appropriate time weights.

math.AP↗

arXiv2019

Global well-posedness of magnetohydrodynamic equations

We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the magnetic field is subject to a time-dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to (1.1)-(1.4). Then we derive the existence of a uniform attractor for (1.1)-(1.4).

math.AP↗