Local existence and Gevrey regularity of 3-D Navier–Stokes equations with ℓp initial data

We obtain local existence and Gevrey regularity of 3-D periodic Navier–Stokes equations in case the sequence of Fourier coefficients of the initial data is in . The ℓp norm of the sequence of Fourier coefficients of the solution and its analogous Gevrey norm remains bounded on a time interval whose length depends only on the size of the body force and the ℓp norm of the Fourier coefficient sequence of the initial data. The control on the Gevrey norm produces explicit estimates on the analyticity radius of the solution as in Foias and Temam (J. Funct. Anal. 87 (1989) 359–369). The results provide an alternate approach in estimating the space-analyticity radius of solutions to Navier–Stokes equations than the one presented by Grujić and Kukavica (J. Funct. Anal. 152 (1998) 447–466).