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- W1978797918 abstract "The nonlinear Schrodinger equation , , arises from a Hamiltonian on infinite-dimensional phase space . For , Bourgain (Comm. Math. Phys. 166 (1994), 1–26) has shown that there exists a Gibbs measure on balls in phase space such that the Cauchy problem for is well posed on the support of , and that is invariant under the flow. This paper shows that satisfies a logarithmic Sobolev inequality (LSI) for the focusing case and on for all N>0; also satisfies a restricted LSI for on compact subsets of determined by Holder norms. Hence for p = 4, the spectral data of the periodic Dirac operator in with random potential subject to are concentrated near to their mean values. The paper concludes with a similar result for the spectral data of Hill's equation when the potential is random and subject to the Gibbs measure of Korteweg–de Vries." @default.
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- W1978797918 date "2014-03-19" @default.
- W1978797918 modified "2023-09-27" @default.
- W1978797918 title "Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation" @default.
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- W1978797918 doi "https://doi.org/10.1080/17442508.2014.882924" @default.
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