Well-posedness for the periodic Hyperbolic nonlinear Schrödinger equations

2025/10/03 by Engin Başakoğlu, Yuzhao Wang, Başakoğlu, Engin +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2510.03211

Abstract

We establish local well-posedness for the hyperbolic nonlinear Schrodinger equation (HNLS) in the critical spaces. Following the approach of Killip and Visan, we derive scale-invariant Strichartz estimates for HNLS on both rational and irrational tori, thereby removing the epsilon-loss of derivative present in the hyperbolic Strichartz estimates of Bourgain and Demeter.

Citations

• Sharp unconditional well-posedness of the 2-d periodic cubic hyperbolic nonlinear Schrödinger equation
• A remark on norm inflation for nonlinear Schrödinger equations
• The profile decomposition for the hyperbolic Schrödinger equation
• Strichartz estimates for non-degenerate Schrödinger equations
• Global Well-Posedness of 2D Non-Focusing Schrödinger Equations via Rigorous Modulation Approximation
• The proof of the l² Decoupling Conjecture
• Scale invariant Strichartz estimates on tori and applications
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
• Strichartz estimates for non elliptic Schrödinger equations on compact manifolds
• Strichartz estimates for Schrödinger equations on irrational tori
• Strichartz estimates for the periodic non elliptic Schrodinger equation
• Periodic Cubic Hyperbolic Schrödinger equation on \T²
• Remark on the periodic mass critical nonlinear Schrödinger equation
• Multisplitting and collapse of self-focusing anisotropic beams in normal/anomalous dispersive media

Related

• Hyperbolic nonlinear Schrödinger equations on ℝ× \mathbbT
• Periodic nonlinear Schrödinger equation in critical H^s(\Tⁿ) spaces
• Periodic Cubic Hyperbolic Schrödinger equation on \T²
• Sharp unconditional well-posedness of the 2-d periodic cubic hyperbolic nonlinear Schrödinger equation
• On sharp Strichartz estimate for hyperbolic Schrödinger equation on \mathbbT³