Probabilistically Strong Solutions to Stochastic Euler Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910005004861440 |
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| author | Gess, Benjamin Lasarzik, Robert |
| author_facet | Gess, Benjamin Lasarzik, Robert |
| contents | In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically strong solutions for the stochastic incompressible Euler equations. In particular, this solves the open problem of constructing probabilistically strong solutions for the stochastic Euler equations that satisfy the energy inequality for general $L^2$ initial data. We introduce the concept of energy-variational solutions in the stochastic context in order to treat the nonlinearities without changing the probability space. Furthermore, we extend these results to fluids driven by transport noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22073 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probabilistically Strong Solutions to Stochastic Euler Equations Gess, Benjamin Lasarzik, Robert Analysis of PDEs 60H15, 35R60, 35D99, 76B03, 35Q35 In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically strong solutions for the stochastic incompressible Euler equations. In particular, this solves the open problem of constructing probabilistically strong solutions for the stochastic Euler equations that satisfy the energy inequality for general $L^2$ initial data. We introduce the concept of energy-variational solutions in the stochastic context in order to treat the nonlinearities without changing the probability space. Furthermore, we extend these results to fluids driven by transport noise. |
| title | Probabilistically Strong Solutions to Stochastic Euler Equations |
| topic | Analysis of PDEs 60H15, 35R60, 35D99, 76B03, 35Q35 |
| url | https://arxiv.org/abs/2601.22073 |