Multiwavelet characterization of function spaces adapted to the Navier-Stokes equations
Joseph D. Lakey, Sofian Talal Obeidat, María Cristina Pereyra · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
We use wavelets based ona modification of the Geronimo- Hardin-Massopust construction to define localized extension/restriction operators form half-spaces to their full spaces/boundaries respectively. These operations are continuous in Sobolev and Morrey space norms. We also prove estimates for multiresolution projections of pointwise products of functions in these spaces. These are two of the key steps in extending results of Federbush and of Cannone and Meyer concerning solutions of Navier-Stokes with initial data in Sobolev and Morrey spaces to the case of half spaces and, ultimately, to more general domains with boundary.