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Preprints, Working Papers, ... Year : 2023

The logarithmic Schrödinger equation with spatial white noise on the full space

Abstract

We solve the Schrödinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d ≤ 2. Because of the nonlinearity, the regularity structures and the paracontrolled calculus can not be used. To solve the equation, we rely on an exponential transform that has proven useful in the context of other singular SPDEs.
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hal-04189989 , version 1 (29-08-2023)

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Quentin Chauleur, Antoine Mouzard. The logarithmic Schrödinger equation with spatial white noise on the full space. 2023. ⟨hal-04189989⟩
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