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arXiv · 2603.00957

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

Chengfei Ai·Mengxing Bei·Yong Wang
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Abstract

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.

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Chengfei Ai, Mengxing Bei, Yong Wang. 2026-03-01. Global solutions of the 3D inhomogeneous incompressible viscoelastic system without structure assumptions. https://arxiv.org/abs/2603.00957

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