9 problems

Let $\operatorname{AdS}_3$ denote three-dimensional Anti-de Sitter space, and consider small smooth perturbations whose spatial dependence admits a radius of analyticity $\rho(t)$,…

Let $(u_0,0,T)$ be a smooth periodic set of data. Global regularity for homogeneous periodic data with normalised pressure. There exists a smooth periodic solution $(u,p,u_0,0,T)$…

Let $(u_0,f,T)$ be an $H^1$ set of data such that, for every multi-index $\alpha$ and every compact $K\subset\mathbf{R}^3$, … and … Global well-posedness from spatially smooth…

Let $(u_0,f,T)$ be $H^1$ data and let an $H^1$ mild solution be a solution with $u\in L^\infty_tH^1_x\cap L^2_tH^2_x$ and the corresponding pressure and Duhamel formulation. Global…

Let $(u_0,0,T)$ be a smooth homogeneous $H^1$ set of data. An almost smooth finite energy solution is smooth for positive times and has the stated continuous spatial and time-deriv…

Let $(u_0,f,T)$ be a smooth periodic set of data. A periodic solution has normalised pressure when its pressure satisfies the normalisation used in the periodic Navier–Stokes formu…

Let $(u_0,f,T)$ be a smooth periodic set of data. Global regularity for periodic data. There exists a smooth periodic solution $(u,p,u_0,f,T)$ with the indicated data. This is the…

Let $(u_0,0,T)$ be a homogeneous Schwartz set of data. Global regularity for homogeneous Schwartz data. There exists a smooth finite energy solution $(u,p,u_0,0,T)$ with the indica…

Let ${\mathcal S}$ be the space of classical data $(\phi_0,\phi_1)$, where $\phi_0:{\mathbf R}^2\to{\mathbf H}$ is Schwartz modulo constants and…