The logarithmic Schr\"odinger equation with spatial white noise on the full space
Abstract
We solve the Schr\"odinger 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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