# An Eulerian-Lagrangian approach for incompressible fluids: Local theory

@article{Constantin2000AnEA, title={An Eulerian-Lagrangian approach for incompressible fluids: Local theory}, author={Peter Constantin}, journal={Journal of the American Mathematical Society}, year={2000}, volume={14}, pages={263-278} }

We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial differential equations.

## 97 Citations

An Eulerian–Lagrangian Approach¶to the Navier–Stokes Equations

- Mathematics
- 2000

Abstract: We present a formulation of the incompressible viscous Navier–Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a…

Euler and Navier-Stokes Equations

- Mathematics, Philosophy
- 2008

We present results concerning the local existence, regularity and possible
blow up of solutions to incompressible Euler and Navier-Stokes equations.

A Variational Formulation for the Navier-Stokes Equation

- Mathematics
- 2005

In this paper we prove a new variational principle for the Navier-Stokes equation which asserts that its solutions are critical points of a stochastic control problem in the group of area-preserving…

Stochastic Mean-Field Approach to Fluid Dynamics

- MathematicsJ. Nonlinear Sci.
- 2018

It is shown that the incompressible Navier–Stokes equation can be derived from an infinite-dimensional mean-field stochastic differential equation.

ON A VARIATIONAL PRINCIPLE FOR THE NAVIER-STOKES EQUATION

- Mathematics
- 2007

In this paper we study the variational principle for the Navier-Stokes equation described in [Gom05], and clarify the role of boundary conditions. We show that in certain special cases this…

Stochastic formulation of incompressible fluid flows in wall bounded regions

- Mathematics
- 2022

The goal of the article is to establish a mathematical theory which may be used to design MonteCarlo simulations of the dynamics of time irreversible reaction-diffusions and incompressible fluid…

TRANSPORT IN VISCOUS ROTATING FLUIDS

- Geology
- 2004

We consider a uniformly rotating viscous incompressible fluid and estimate particle transport in the vertical direction (parallel to the rotation axis). We prove that for short time and regular…

Transport in Viscous Rotating Fluids

- Geology
- 2004

We consider a uniformly rotating viscous incompressible fluid and estimate particle transport in the vertical direction (parallel to the rotation axis). We prove that for short time and regular…

GLOBAL EXISTENCE FOR NAVIER-STOKES WITH SMALL REYNOLDS

- Mathematics
- 2008

We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of…

On the blow-up problem for the Euler equations andthe Liouville type results in the fluid equations

- Mathematics
- 2013

In this paper we briefly review recent results mostly by the author
related to the blow-up problem of the 3D Euler equations and the
Liouville type results in the various equations of the fluids.

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