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Global \(H^1\) solvability of the 3D logarithmic Schrödinger equation. (English) Zbl 1180.81071

Summary: We investigate the existence of a unique global mild solution in \(H^1(\mathbb R^3)\) of the initial-boundary value problem associated with the logarithmic Schrödinger equation i\(\partial _t \psi = -D \Delta \psi +\sigma \log (|\psi|^2)\), with \(D>0\) and \(\sigma \in \mathbb R\setminus \{0\}\).

MSC:

81Q80 Special quantum systems, such as solvable systems
81U15 Exactly and quasi-solvable systems arising in quantum theory
35Q55 NLS equations (nonlinear Schrödinger equations)
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