Lq Helmholtz decomposition and Lq spectral theory for the Maxwell operator on periodic domains
We investigate the Helmholtz decomposition on periodic domains and prove the existence of the Lq Helmholtz decomposition on periodic domains for a suitable range of q depending on the regularity of the boundary. As applications, we prove a spectral multiplier theorem for a Maxwell type operator and study the incompressible Navier Stokes equations on periodic domains in the Lq setting.