Remarks on hypoelliptic equations

Many results of smooth hypoellipticity are available for scalar equations. Much remains to be done for systems and/or at different levels of regularity and in particular for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -hypoellipticity. In this article we provide some examples and counter-examples.

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Publication Details

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Annales Henri Lebesgue
Published
2026-03-17
DOI
https://doi.org/10.5802/ahl.261
Primary Topic
Navier-Stokes equation solutions
Type
article
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article

Remarks on hypoelliptic equations

Nicolas Burq, Valeria Banica
Annales Henri Lebesgue
Navier-Stokes equation solutions
article

Remarks on hypoelliptic equations

Nicolas Burq, Valeria Banica
article en

Abstract

Many results of smooth hypoellipticity are available for scalar equations. Much remains to be done for systems and/or at different levels of regularity and in particular for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -hypoellipticity. In this article we provide some examples and counter-examples.

Annales Henri LebesgueVol. 9
Centre National de la Recherche Scientifique (FR), Institut Universitaire de France (FR), Université Paris-Saclay (FR), Laboratoire de Mathématiques d'Orsay (FR), Sorbonne Université (FR), Laboratoire Jacques-Louis Lions (FR)
Openalex Percentile: Top 16%
Navier-Stokes equation solutions
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