Local-in-time well-posedness for Nonlinear Schroedinger equations with potentials
Younghun Hong
TL;DR
This paper establishes the local-in-time well-posedness and conservation laws for a 3D cubic nonlinear Schrödinger equation with a real potential, advancing understanding of its mathematical properties.
Contribution
It proves local well-posedness and conservation laws for NLS with potentials, a novel extension in the analysis of such equations.
Findings
Proved local-in-time well-posedness.
Established mass and energy conservation laws.
Applied to 3D cubic nonlinear Schrödinger equations.
Abstract
We prove the local-in-time well-posedness and the mass and energy conservation laws for a 3d cubic nonlinear Schroedinger equation with a real-valued potential.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Stability and Controllability of Differential Equations