# American Institute of Mathematical Sciences

December  2019, 11(4): 553-560. doi: 10.3934/jgm.2019027

## Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers

 GFMUL and Departamento de Matemática Instituto Superior Técnico, Univ. Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Received  March 2018 Revised  March 2019 Published  November 2019

We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagrange multiplier. Moreover we describe how to obtain corresponding constants of the motion.

Citation: Ana Bela Cruzeiro. Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers. Journal of Geometric Mechanics, 2019, 11 (4) : 553-560. doi: 10.3934/jgm.2019027
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