Global in time solution to the incompressible Euler Equations on $R^n$. An elementary approach.

Ulisse Iotti (1)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

In this paper we prove a theorem of global time-extension for the local classical solution of Euler's evolution problem in $R^n$ with $n \geqslant 2$ for incompressible fuids subjected to external forces and regular initial conditions. This will be achieved by expressing the boundedness of the time derivative of the $L^\infty$ solution norm.

Mots clés: Euler equations; Navier-Stokes equations; global existence; blow-up; regularity; nonlinear PDE; flow; fluid dynamics

Domaines: Equations aux dérivées partielles [math.AP]

Ulisse Iotti. Global in time solution to the incompressible Euler Equations on $R^n$. An elementary approach.. 2011. ⟨hal-00608010v5⟩