PreprintarXiv licencearXiv
Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion
Abstract
We study the 3-D incompressible inviscid Oldroyd-B model with fractional stress diffusion (−Δ)βτ and without stress damping. For β∈ (1/2,1) and s∈ [2β+1/2,5/2], we establish local well-posedness for initial data (u0,τ0) in Hs(ℝ3), provided that |(u0,τ0)|Hβ is bounded and |Λβ(u0,τ0)|Hs−β is sufficiently small. If, in addition, β∈(1/2,5/6], we give a global well-posedness result. Our results complement the work of Constantin, Wu, Zhao and Zhu \cite{ConstantinWuZhaoZhu2021} by treating the Sobolev regularity s∈[2β+1/2,5/2], below the threshold s>5/2 considered there. We also provide an ℓ2 alternative to the high-frequency ℓ1 summability condition in the framework of Wu and Zhao \cite{WuZhao2022}.
Related
- A Good-Vorticity Low-Regularity Integrator for the Inviscid Oldroyd--B System with Stress Diffusion
- Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion
- Regularity of the solution map for the Oldroyd--B model with fractional stress dissipation
- Global-in-time inviscid limit of the Navier-Stokes equations for vortex-wave data
- A Necessary and Sufficient Condition for the Existence of Global Smooth Solutions to the One-Dimensional Inviscid Burgers-Vlasov System
BibTeX
@misc{lu2026global,
title = {{Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion}},
author = {Yi Lu and Chen Liang and Zhaoyang Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21473},
eprint = {2610.21473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21473},
}
RIS
TY - UNPB
TI - Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion
AU - Yi Lu
AU - Chen Liang
AU - Zhaoyang Yin
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21473
UR - https://arxiv.org/abs/2610.21473
AB - We study the 3-D incompressible inviscid Oldroyd-B model with fractional stress diffusion (−Δ)^βτ and without stress damping. For β∈ (1/2,1) and s∈ [2β+1/2,5/2], we establish local well-posedness for initial data (u_0,τ_0) in H^s(ℝ^3), provided that |(u_0,τ_0)|_H^β is bounded and |Λ^β(u_0,τ_0)|_H^s−β is sufficiently small. If, in addition, β∈(1/2,5/6], we give a global well-posedness result. Our results complement the work of Constantin, Wu, Zhao and Zhu \cite{ConstantinWuZhaoZhu2021} by treating the Sobolev regularity s∈[2β+1/2,5/2], below the threshold s>5/2 considered there. We also provide an ℓ^2 alternative to the high-frequency ℓ^1 summability condition in the framework of Wu and Zhao \cite{WuZhao2022}.
ER -