Weil-Petersson Teichmüller space II: smoothness of flow curves of $H^{\frac{3}{2}}$-vector fields

Yuliang Shen, Shuan Tang

Given a continuous vector field $\lambda (t,\cdot )$ of Sobolev class $H^{\frac{3}{2}}$ on the unit circle $S^1$, the flow maps $\eta =g(t,\cdot )$ of the differential equation $$ \cases \frac{d…