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- W2614271526 abstract "Abstract We study the nonlinear Schrödinger equation posed on product spaces <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mi>ℳ</m:mi> <m:mi>k</m:mi> </m:msup> </m:mrow> </m:math> {{mathbb{R}}^{n}times{mathcal{M}}^{k}} , for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {ngeq 1} and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {kgeq 1} , with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>ℳ</m:mi> <m:mi>k</m:mi> </m:msup> </m:math> {{mathcal{M}}^{k}} any k -dimensional compact Riemannian manifold. The main results concern global well-posedness and scattering for small data solutions in non-isotropic Sobolev fractional spaces. In the particular case of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {k=2} , <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {H^{1}} -scattering is also obtained." @default.
- W2614271526 created "2017-05-26" @default.
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- W2614271526 date "2017-05-18" @default.
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- W2614271526 title "Well-posedness and scattering for the mass-energy NLS on ℝ<sup> <i>n</i> </sup> × ℳ<sup> <i>k</i> </sup>" @default.
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- W2614271526 doi "https://doi.org/10.1515/anly-2016-0013" @default.
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