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We show, by the means of several examples, how we can use Gibbs measures to construct global solutions to dispersive equations at low regularity.
Low regularity local well-posedness of the derivative nonlinear Schrödinger equation with periodic initial data
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Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
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Invariant measures for the Nonlinear Schrödinger equation on the disc
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Effective integrable dynamics for some nonlinear wave equation
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On unconditional well-posedness of modified KdV
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Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
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On the one-dimensional cubic nonlinear Schrödinger equation below L 2 L^{2}
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Random data Cauchy theory for supercritical wave equations II: A global existence result
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Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
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Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case
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Probabilistic well-posedness for the cubic wave equation
N. Burq and N. Tzvetkov · 2014
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Invariant measures and long time behaviour for the Benjamin-Ono equation I
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Invariant measures and long time behaviour for the Benjamin-Ono equation II
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