Well-posedness and ill-posedness results for the Novikov-Veselov equation

Yannis  Angelopoulos

doi:10.3934/cpaa.2016.15.727

Article Contents

2016, Volume 15, Issue 3: 727-760. Doi: 10.3934/cpaa.2016.15.727

This issue Previous Article On Compactness Conditions for the $p$-Laplacian Next Article A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space

Well-posedness and ill-posedness results for the Novikov-Veselov equation

Yannis Angelopoulos^1,

1.
Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George Street, Toronto, On M5S 2E4

Received: August 31, 2014

Revised: November 30, 2015

Published: April 2016

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Abstract

In this paper we study the Novikov-Veselov equation and the related modified Novikov-Veselov equation in certain Sobolev spaces. We prove local well-posedness in $H^s (\mathbb{R}^2)$ for $s > \frac{1}{2}$ for the Novikov-Veselov equation, and local well-posedness in $H^s (\mathbb{R}^2)$ for $s > 1$ for the modified Novikov-Veselov equation. Finally we point out some ill-posedness issues for the Novikov-Veselov equation in the supercritical regime.

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Mathematics Subject Classification: 35Q53.

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