15:{"metadata":[["$","title","0",{"children":"Nonlinear Schrödinger equation, differentiation by parts and modulation spaces"}],["$","meta","1",{"name":"description","content":"We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schr\\\"odinger equation in the modulation space $M_{p,q}^{s}(\\mathbb R)$ where $1\\leq q\\leq2$, $2\\leq p<\\frac{10q'}{q'+6}$ and $s\\geq0$. Moreover, for either $1\\leq q\\leq\\frac32, s\\geq0$ and $2\\leq p\\leq 3$ or $\\frac32\\frac23-\\frac1{q}$ and $2\\leq p\\leq 3$ or $\\frac{18}{11}\\frac23-\\frac1{q}$ and $2\\leq p<\\frac{10q'}{q'+6}$ we show that the Cauchy problem is unconditionally wellposed in $M_{p,q}^{s}(\\mathbb R).$ This improves \\cite{NP}, where the case $p=2$ was considered and the differentiation by parts technique was introduced to a problem with continuous Fourier variable. Here the same technique is used, but more delicate estimates are necessary for $p\\neq2$."}],["$","meta","2",{"name":"author","content":"Leonid Chaichenets"}],["$","meta","3",{"name":"author","content":"Dirk Hundertmark"}],["$","meta","4",{"name":"author","content":"Peer Kunstmann"}],["$","meta","5",{"name":"author","content":"Nikolaos Pattakos"}],["$","meta","6",{"name":"keywords","content":"Analysis of PDEs"}],["$","meta","7",{"name":"referrer","content":"origin"}],["$","meta","8",{"name":"robots","content":"index, follow"}],["$","link","9",{"rel":"canonical","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3"}],["$","link","10",{"rel":"alternate","hrefLang":"de-DE","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3/de"}],["$","link","11",{"rel":"alternate","hrefLang":"fr-FR","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3/fr"}],["$","link","12",{"rel":"alternate","hrefLang":"es-ES","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3/es"}],["$","link","13",{"rel":"alternate","hrefLang":"it-IT","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3/it"}],["$","link","14",{"rel":"alternate","hrefLang":"ru-RU","href":"https://synthical.com/article/Nonlinear-Schr%C3%B6dinger-equation%2C-differentiation-by-parts-and-modulation-spaces-222d3ec0-ffb3-11ed-9b54-72eb57fa10b3/ru"}],["$","meta","15",{"property":"og:title","content":"Nonlinear Schrödinger equation, differentiation by parts and modulation spaces"}],["$","meta","16",{"property":"og:description","content":"We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schr\\\"odinger equation in the modulation space $M_{p,q}^{s}(\\mathbb R)$ where $1\\leq q\\leq2$, $2\\leq p<\\frac{10q'}{q'+6}$ and $s\\geq0$. 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