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Math Physics Seminar
Date: Thursday, September 17
Time: 3:00-4:00 PM
Location: TBA
Speaker: MS. Raiba Chowdhury (Georgia Southern University)
Title: Rotational Damped Nonlinear Schrödinger Equation with Stark Potential
Abstract: We study the focusing nonlinear Schrödinger equation with an added Stark potential, a rotation term, and linear damping. These perturbations break the mass, energy, momentum, and angular momentum identities of the classical equation, and we derive the evolution law each one satisfies instead. We then construct a generalized Avron–Herbst transformation, an explicit change of variables removing the Stark and rotational terms simultaneously, which reduces the equation to a damped, mass-critical focusing NLS equation with an already established threshold theorem.
Transferring this threshold back, we show that the sharp mass threshold ‖Q‖ L² for global existence is independent of both the rotation and the Stark field, and that the classical log-log blow-up rate above threshold is unaffected by damping, due to an exact cancellation between the transformation's own damping factor and the damping already present in the underlying threshold theorem. A separate concentration argument, independent of the transformation, shows that blow-up solutions must concentrate at least the ground-state mass at the singularity, giving a second proof of global existence valid in every dimension along with an explicit bound on the blow-up time.
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