On the Cauchy problem for logarithmic fractional Schrödinger equation
arxiv(2024)
摘要
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.
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