On the Cauchy problem for logarithmic fractional Schr{ö}dinger equation
Abstract
We consider the fractional Schrodinger equation with a logarithmic nonlinearity, when the power of the Laplacian is between zero and one. We prove global existence results in three different functional spaces: the Sobolev space corresponding to the quadratic form domain of the fractional Laplacian, the energy space, and a space contained in the operator domain of the fractional Laplacian. For this last case, a finite momentum assumption is made, and the key step consists in estimating the Lie commutator between the fractional Laplacian and the multiplication by a monomial.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.06816
 arXiv:
 arXiv:2404.06816
 Bibcode:
 2024arXiv240406816C
 Keywords:

 Mathematics  Analysis of PDEs