Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$
Xueying Yu, Haitian Yue, Zehua Zhao
Abstract
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schr\"odinger equation on the product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below the threshold that arises from the the ground state in the Euclidean setting. The defocusing analogue was discussed and proved in Ionescu-Pausader \cite{IPRT3} (Comm. Math. Phys. 312 (2012), no. 3, 781-831).
Topics & Concepts
MathematicsProduct (mathematics)Mathematical analysisSpace (punctuation)Euclidean spaceNonlinear systemProduct topologyEuclidean geometryGround stateState (computer science)Two-dimensional spaceEuclidean distanceState spaceCubic functionCartesian productNon-Euclidean geometryInitial value problemTriple productPure mathematicsAdvanced Mathematical Physics ProblemsNonlinear Waves and SolitonsMathematical Analysis and Transform Methods