Euler-Lagrangian approach to 3D stochastic Euler equations

Flandoli Franco; Luo Dejun

doi:10.3934/jgm.2019008

Article Contents

2019, Volume 11, Issue 2: 153-165. Doi: 10.3934/jgm.2019008

This issue Previous Article Particle relabelling symmetries and Noether's theorem for vertical slice models Next Article Riemann-Hilbert problem, integrability and reductions

Euler-Lagrangian approach to 3D stochastic Euler equations

Flandoli Franco^1, , and
Luo Dejun^2,3,

1.
Scuola Normale Superiore of Pisa, Piazza dei Cavalieri, 7, 56124 Pisa, Italy
2.
Key Laboratory of Random Complex Structures and Data Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing 100049, China

^* Corresponding author: Franco Flandoli
^* Corresponding author: Franco Flandoli

Received: March 2018

Revised: February 2019

Published: June 2019

The second author is supported by the National Natural Science Foundation of China (Nos. 11431014, 11571347) and the Youth Innovation Promotion Association, CAS (2017003).

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Abstract

3D stochastic Euler equations with a special form of multiplicative noise are considered. A Constantin-Iyer type representation in Euler-Lagrangian form is given, based on stochastic characteristics. Local existence and uniqueness of solutions in suitable Hölder spaces is proved from the Euler-Lagrangian formulation.

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Mathematics Subject Classification: Primary: 35Q31; Secondary: 76B03.

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