Euler–Lagrangian Approach to Stochastic Euler Equations in Sobolev Spaces

The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based on Ito–Wentzell–Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrang...

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Veröffentlicht in:	Journal of mathematical fluid mechanics 2023-08, Vol.25 (3), Article 61
Hauptverfasser:	Olivera, Christian, Londoño, Juan D.
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Continuum Physics Euler-Lagrange equation Eulers equations Fluid mechanics Fluid- and Aerodynamics Formulations Mathematical analysis Mathematical Methods in Physics Physics Physics and Astronomy Sobolev space Theoretical mathematics
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Beschreibung
Zusammenfassung:	The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based on Ito–Wentzell–Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrangian formulation in suitable Sobolev Spaces.
ISSN:	1422-6928 1422-6952
DOI:	10.1007/s00021-023-00808-5