Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion

We study the 3-D incompressible inviscid Oldroyd-B model with fractional stress diffusion \((-Δ)^βτ\) and without stress damping. For $β\in (\frac{1}{2},1)$ and $s\in [2β+\frac{1}{2},\frac{5}{2}]$, we establish local well-posedness for initial data $(u_0,τ_0)$ in \(H^s(\mathbb R^3)\), provided that