Strichartz estimates and small data for the nonlinear Schrödinger equation

2014 ◽  
pp. 23-39
Author(s):  
Herbert Koch ◽  
Daniel Tataru ◽  
Monica Vişan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Strichartz Estimates ◽  
Small Data ◽  
Nonlinear Schrödinger

scholarly journals Growth of Solutions to NLS on Irrational Tori

2017 ◽  
Vol 2019 (9) ◽  
pp. 2919-2950 ◽  
Author(s):  
Yu Deng ◽  
Pierre Germain
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Strichartz Estimates ◽  
Nonlinear Schrödinger ◽  
Quintic Nonlinearity ◽  
Polynomial Bounds ◽  
Growth Of Solutions

Abstract We prove polynomial bounds on the $H^s$ growth for the nonlinear Schrödinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.

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