Work

On the Cauchy problem for logarithmic fractional Schrödinger equation

Year: 2024

Type: article

Abstract: We consider the fractional Schrödinger 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.

Source: Portugaliae Mathematica

DOI: 10.4171/pm/2133

Authors: Rémi Carles, Fangyuan Dong

Institutions: Centre National de la Recherche Scientifique, Université de Rennes

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Centre Henri Lebesgue, Agence Nationale de la Recherche

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, G5539822453