## On the Helicity conservation for the incompressible Euler equations

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- by Luigi De Rosa PDF
- Proc. Amer. Math. Soc.
**148**(2020), 2969-2979 Request permission

## Abstract:

In this work we investigate the helicity regularity for weak solutions of the incompressible Euler equations. To prove regularity and conservation of the helicity we will treat the velocity $u$ and its $\operatorname {curl} u$ as two independent functions and we mainly show that the helicity is a constant of motion assuming $u \in L^{2r}_t(C^\theta _x)$ and $\operatorname {curl} u \in L^{\kappa }_t(W^{\alpha ,1}_x)$, where $r,\kappa$ are conjugate Hölder exponents and $2\theta +\alpha \geq 1$. Using the same techniques we also show that the helicity has a suitable Hölder regularity even in the range where it is not necessarily constant.## References

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## Additional Information

**Luigi De Rosa**- Affiliation: EPFL SB, Station 8, CH-1015 Lausanne, Switzerland
- MR Author ID: 1282108
- Email: luigi.derosa@epfl.ch
- Received by editor(s): March 15, 2019
- Received by editor(s) in revised form: November 1, 2019, and November 18, 2019
- Published electronically: February 26, 2020
- Communicated by: Catherine Sulem
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 2969-2979 - MSC (2010): Primary 35Q31, 35A01, 35D30
- DOI: https://doi.org/10.1090/proc/14952
- MathSciNet review: 4099784