Matteo Giardi

Ideal MHD below the classical well-posedness threshold

We establish local existence and uniqueness of solutions for the ideal incompressible magnetohydrodynamics system posed on $[0,T]\times\mathbb{R}^n$, $n\ge2$, with a nonzero constant initial magnetic field $\mathbf{B}_0$ and arbitrary divergence-free velocity data $v_0\in H^s$, in the range $(n+1)/2<s\le n/2+1$. The pr...