Lagrangian controllability of inviscid perfect fluids: a constructive approach

TL;DR

This paper introduces a constructive method for Lagrangian controllability of inviscid perfect fluids, focusing on numerical approaches and stability analysis, with potential applications in fluid control simulations.

Contribution

It presents a new constructive approach for Lagrangian controllability of the Euler equation, including numerical methods and stability insights for bi-dimensional fluids.

Findings

Develops a constructive control method for Euler equations

Analyzes numerical stability issues in simplified models

Proposes rational function approximation techniques

Abstract

We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal com- putations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyse through a simplified problem the observed instabilities.