On local well-posedness of the stochastic incompressible density-dependent Euler equations

Claudia Espitia; David A. C. Mollinedo; Christian Olivera

On local well-posedness of the stochastic incompressible density-dependent Euler equations

Analysis of PDEs 2025-10-28 v3

Authors: Claudia Espitia , David A. C. Mollinedo , Christian Olivera

Abstract

In this paper we study the stochastic inhomogeneous incompressible Euler equations in the whole space $\RR^3$ . We prove the existence and pathwise uniqueness of local solutions with both additive and multiplicative stochastic noise. Our approach is based on reducing our problem to a random problem and some estimations for type transport equations.

Keywords

stochastic Euler equations inhomogeneous incompressible local well-posedness additive noise multiplicative noise pathwise uniqueness

Cite

@article{arxiv.2406.06161,
  title  = {On local well-posedness of the stochastic incompressible density-dependent Euler equations},
  author = {Claudia Espitia and David A. C. Mollinedo and Christian Olivera},
  journal= {arXiv preprint arXiv:2406.06161},
  year   = {2025}
}

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