Gevrey regularity of solutions to the 3-D Navier-Stokes equations with weighted lₚ initial data

We prove the existence and Gevrey regularity of local solutions of the three dimensional periodic Navier-Stokes equations in case the sequence of Fourier coefficients of the initial data lies in an appropriate weighted lp space. Our work is motivated by that of Foias and Temam ([10]) and we obtain a generalization of their result. In particular, our analysis allows for initial data that are less smooth than in [10] and can also have infinite energy. Our main tool is a variant of the Young convolution inequality enabling us to estimate the nonlinear term in weighted lp norm.