Mathematical aspects of nonlinear dispersive equations

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Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations (2011, methodology): “For analytical estimates it was convenient in [24] and [20] to consider ρ as measure either on the Hilbert space H(T) (Sobolev space) for arbitrary σ < 1/2 or as a measure on the Banach space FL(T) (FourierLebesgue space [14, 9, 6]) with norm ‖u‖FLs,r(T) := ‖ 〈n〉 s û ‖lrn(Z) and with the conditions ”
Global parametrices and dispersive estimates for variable coefficient wave equations (2007, result): “Strichartz estimates for Schrödinger equations with variable coefficients.”
Local decay of waves on asymptotically flat stationary space-times (2009, unknown): “CA 94720-3840”
Strichartz estimates for Schrödinger equations on irrational tori (2013, methodology): “Our proof follows the ideas developed in [6].”
INVARIANT WEIGHTED WIENER MEASURES AND ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE PERIODIC DERIVATIVE NLS. (2010, background): “[27, 21, 14, 22]) and scaling like H 1/2 ✏(T), for small ✏ > 0.”
Global Smoothing for the Periodic KdV Evolution (2011, unknown): “In [5], Christ obtained a (local-in-time) smoothing estimate in the F`p → F`q setting for 1d cubic NLS.”