3 problems

Let $\mathcal{S}_{even}(\mathbb{R})$ denote the space of real-valued even Schwartz functions on $\mathbb{R}$, and let $\widehat{f}$ be the Fourier transform of $f$. For a sequence…

Let $\phi\in\mathcal{S}(\mathbb{R})\setminus\{0\}$, and let a finite wavelet system generated by $\phi$ be a finite collection of wavelet dilates and translates of $\phi$. Finite-w…

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…