Evolution equation with fractional Schrödinger operators: monotonicity and exponential decay of solutions in Morrey spaces

2025/12/15 by Jan W. Cholewa, Cholewa, Jan W., Anı́bal Rodriguez-Bernal +1
Mathematics · #Nonlinear Partial Differential Equations #Fractional Differential Equations Solutions #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2512.13499

Abstract

We consider evolution equation with fractional Schrödinger operators in Morrey spaces. We prove order preserving properties of the associated semigroup in Morrey scale. We prove monotonicity of the semigroup with respect to Morrey's potentials and give some precise estimates of its exponential growth. We show that Arendt and Batty's type condition on the potential is necessary for exponential decay of Morrey's norms of the semigroup and find a large class of dissipative potentials for which it is also sufficient.

Citations

• On linear Schrödinger parabolic problems in Morrey spaces
• Exponential decay for fractional Schrödinger parabolic problems
• Fractional Laplacian with Hardy potential
• Optimal Existence and Uniqueness Theory for the Fractional Heat Equation

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