Resumen de On the wellposedness of the KdV equation on the space of pseudomeasures

Thomas Kappeler, Jan Molnar

• In this paper we prove a wellposedness result of the KdV equation on the space of periodic pseudomeasures, also referred to as the Fourier Lebesgue space F∞(T, R), where F∞(T, R)is endowed with the weak* topology. Actually, it holds on any weighted Fourier Lebesgue space Fs,∞(T, R) with −1/2 < s ≤ 0 and improves on a wellposedness result of Bourgain for small Borel measures as initial data. A key ingredient of the proof is a characterization for a distribution q in the Sobolev space H−1(T, R) to be in F∞(T, R) in terms of asymptotic behavior of spectral quantities of the Hill operator −∂2 x +q. In addition, wellposedness results for the KdV equation on the Wiener algebra are proved.