Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian

Zhenqiu Zhang; Shijun Zheng

Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian

Zhenqiu Zhang
, Shijun Zheng

Mathematical Sciences

Nankai University, China

Research output: Contribution to book or proceeding › Chapter

Abstract

We obtain Strichartz estimates for the linear Schrödinger equation associated with the twisted sub-Laplacian on Cⁿ. As a consequence, we prove the local wellposedness for semilinear Schrödinger equation with polynomial nonlinearity in certain magnetic field.

Original language	American English
Title of host publication	Proceedings of the Centre for Mathematics and Its Applications
State	Published - Jan 1 2010

Disciplines

Education
Mathematics

Keywords

Schroedinger equation
Strichartz estimate
Twisted sub-Laplacian

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https://projecteuclid.org/proceedings/proceedings-of-the-centre-for-mathematics-and-its-applications/The-AMSIANU-Workshop-on-Spectral-Theory-and-Harmonic-Analysis/Chapter/Strichartz-Estimates-and-Local-Wellposedness-for-the-Schr%c3%b6dinger-Equation-with/pcma/1416320880

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Zhang, Z., & Zheng, S. (2010). Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian. In Proceedings of the Centre for Mathematics and Its Applications https://projecteuclid.org/proceedings/proceedings-of-the-centre-for-mathematics-and-its-applications/The-AMSIANU-Workshop-on-Spectral-Theory-and-Harmonic-Analysis/Chapter/Strichartz-Estimates-and-Local-Wellposedness-for-the-Schr%c3%b6dinger-Equation-with/pcma/1416320880

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title = "Strichartz Estimates and Local Wellposedness for the Schr{\"o}dinger Equation with the Twisted Sub-Laplacian",

abstract = "We obtain Strichartz estimates for the linear Schr{\"o}dinger equation associated with the twisted sub-Laplacian on Cn. As a consequence, we prove the local wellposedness for semilinear Schr{\"o}dinger equation with polynomial nonlinearity in certain magnetic field.",

keywords = "Schroedinger equation, Strichartz estimate, Twisted sub-Laplacian",

author = "Zhenqiu Zhang and Shijun Zheng",

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Zhang, Z & Zheng, S 2010, Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian. in Proceedings of the Centre for Mathematics and Its Applications. <https://projecteuclid.org/proceedings/proceedings-of-the-centre-for-mathematics-and-its-applications/The-AMSIANU-Workshop-on-Spectral-Theory-and-Harmonic-Analysis/Chapter/Strichartz-Estimates-and-Local-Wellposedness-for-the-Schr%c3%b6dinger-Equation-with/pcma/1416320880>

TY - CHAP

T1 - Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian

AU - Zhang, Zhenqiu

AU - Zheng, Shijun

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We obtain Strichartz estimates for the linear Schrödinger equation associated with the twisted sub-Laplacian on Cn. As a consequence, we prove the local wellposedness for semilinear Schrödinger equation with polynomial nonlinearity in certain magnetic field.

AB - We obtain Strichartz estimates for the linear Schrödinger equation associated with the twisted sub-Laplacian on Cn. As a consequence, we prove the local wellposedness for semilinear Schrödinger equation with polynomial nonlinearity in certain magnetic field.

KW - Schroedinger equation

KW - Strichartz estimate

KW - Twisted sub-Laplacian

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/257

M3 - Chapter

BT - Proceedings of the Centre for Mathematics and Its Applications

ER -

Strichartz Estimates and Local Wellposedness for the Schrödinger Equation with the Twisted Sub-Laplacian

Abstract

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Keywords

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