Resumen de Periodic Korteweg de Vries equation with measures as initial data

J. Bourgain

• The main result of the paper is that the periodic KdV equation yt+∂3xy+yyx=0 has a unique global solution for initial data y(0) given by a measure μ∈M(T) of sufficiently small norm ∥μ∥ . There are two main ingredients in the proof. The first is the study of the local well-posedness problem in terms of the space-time Fourier-norms as exploited in [Bo] and also subsequent work such as [K-P-V2]. At the end the estimates eventually depend on a uniform estimate in terms of the Fourier coefficients¶¶ supn∈Z,t∈R|y^(n)(t)|