Local well-posedness for the nonlocal derivative nonlinear Schrödinger equation in Besov spaces

2019 ◽  
Vol 187 ◽  
pp. 320-338
Author(s):  
Vanessa Barros ◽  
Roger de Moura ◽  
Gleison Santos
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Besov Spaces ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Well Posedness ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Besov Spaces and Unconditional Well-Posedness for the Nonlinear Schrödinger Equation in $\dot{\rm H}^s({\mathbb R}^n)$

2003 ◽  
Vol 05 (03) ◽  
pp. 349-367 ◽  
Author(s):  
Giulia Furioli ◽  
Elide Terraneo
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Besov Spaces ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Well Posedness ◽  
Extra Condition ◽  
Low Dimensions ◽  
Nonlinear Schrödinger

We extend some results about uniqueness, without any extra condition, of solutions for the nonlinear Schrödinger equation with polynomial nonlinearities in low dimensions. The proof lies on paraproduct techniques and Besov spaces.

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