Low regularity local well-posedness for the zero energy Novikov-Veselov equation

Abstract

The initial value problem u(x, y, 0) = u 0 (x, y) for the zero energy Novikov-Veselov equationis investigated by the Fourier restriction norm method. Local well-posedness is shown in the nonperiodic case for u 0 ∈ H s (R 2 ) with s > − 3 4 and in the periodic case for data u 0 ∈ H s 0 (T 2 ) with mean zero, where s > − 1 5 . Both results rely on the structure of the nonlinearity, which becomes visible with a symmetrization argument. Additionally, for the periodic problem a bilinear Strichartz-type estimate is derived.