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arXiv · 2309.01695

The Cauchy problem for the logarithmic Schr\"odinger equation revisited

Masayuki Hayashi·Tohru Ozawa
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Abstract

We revisit the Cauchy problem for the logarithmic Schr\"odinger equation and construct strong solutions in $H^1$, the energy space, and the $H^2$-energy space. The solutions are provided in a constructive way, which does not rely on compactness arguments, that a sequence of approximate solutions forms a Cauchy sequence in a complete function space and then actual convergence is shown to be in a strong sense.

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Masayuki Hayashi, Tohru Ozawa. 2023-09-04. The Cauchy problem for the logarithmic Schr\"odinger equation revisited. https://doi.org/10.1007/s00023-024-01460-z

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