The ℎ-principle and the equations of fluid dynamics

Abstract

In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov’s <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h"> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding="application/x-tex">h</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-principle holds in several cases.