Abstract
In this paper we analyze the derivative nonlinear Schrödinger equation on with randomized initial data in chosen according to a Wiener measure. We construct an invariant measure at each sufficiently small, fixed mass m through an argument that emulates the divergence theorem in infinitely many dimensions. We also prove that the density function needed to construct the Wiener measure is in Lp, even after scaling of the Fourier coefficients of the initial data.
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