4 problems

Let $s$ denote the Sobolev regularity exponent in Theorem. Sharpness conjecture for the local well-posedness Sobolev range. The range of $s$ in Theorem is sharp for generic problem…

Let $\mathcal G_s(K)$ be the class defined in the paper by, and let $\mathcal F_s(g)$ be the class defined by. For a map $f$, write $K_f$ and $K_{f^{-1}}$ for the distortions of…

Let $0<s<2$ and $1<p<\infty$ satisfy $s<\frac{2}{p}$. Let $\mu,\nu\in F^s_{p,q}\cap L^\infty_c$ satisfy the ellipticity condition, and let $f$ be the principal solution to the Belt…

Let $\omega_0\in H^1(\mathbb{T}^2)\cap L^\infty(\mathbb{T}^2)$ be mean-zero, and let the corresponding solution of the two-dimensional incompressible Euler equations be a Yudovich…