Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms

Seckin Demirbas

doi:10.3934/cpaa.2017072

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2017, Volume 16, Issue 5: 1517-1530. Doi: 10.3934/cpaa.2017072

This issue Previous Article Next Article Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential

Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms

Seckin Demirbas

Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T1Z2 Canada

Received: June 30, 2013

Revised: January 31, 2017

Published: October 2017

The author was partially supported by NSF grants DMS-0900865 and DMS-0901222.

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In this paper we consider the cubic Schrödinger equation in two space dimensions on irrational tori. Our main result is an improvement of the Strichartz estimates on irrational tori. Using this estimate we obtain a local well-posedness result in $H^{s}$ for $s>\frac{131}{416} $. We also obtain improved growth bounds for higher order Sobolev norms.

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Mathematics Subject Classification: 35Q55.

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