A Good-Vorticity Low-Regularity Integrator for the Inviscid Oldroyd--B System with Stress Diffusion

arXiv:2610.41250v1 Announce Type: new Abstract: We establish sharp convergence results for a sequential semi-implicit good-vorticity integrator for the two-dimensional inviscid Oldroyd--B system with stress diffusion on the torus. For exact solutions satisfying $u\in C_tB^{1+\alpha}_{\infty,1}$ and $\tau\in C_tB^\alpha_{\infty,1}\cap L^1_tB^{2+\alpha}_{\infty,1}$, $0\le\alpha\le2$, we prove convergence in the critical norms $B^1_{\infty,1}\times B^0_{\infty,1}$, uniformly over the time nodes on every finite interval where these regularity assumptions hold, including the critical endpoint $\alpha=0$. For $0