On the initial-boundary value problem for the 2D partially dissipative Oldroyd-B model: global well-posedness and large time stability

2025/03/12 by Zhenrong Nong, Nong, Zhenrong, Yinghui Wang +5 · 1 citation
Mathematics · Physics and Astronomy · #35Q35 #76A05 #76A10 #76B03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2503.09067

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space ℝ², the partially periodic domain T×ℝ and the fully periodic torus T², where T represents the one-dimensional periodic torus. Our analysis relies on energy methods to derive key \it a priori estimates that capture the anisotropic regularization induced by horizontal viscosity. Furthermore, for the cases of spatial domains T×ℝ and T², we further investigate the long-time behavior of solutions with small initial data. The compactness along the horizontal direction plays a pivotal role in constructing uniform-in-time estimates, ultimately leading to exponential decay of solutions as t→∞. This decay mechanism reveals how geometric constraints enhance the dissipation in viscoelastic flows.

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