We have constructed Turing complete Navier-Stokes steady states via cosymplectic geometry. You can read it here: arxiv.org/abs/2507.07696

For the curious ones about the Navier-Stokes Turing complete construction, read here: arxiv.org/abs/2507.07696

I'm super excited to learn more about this

The idea of engineering Navier-Stokes flows into a Turing Machine and proving blowup through halting is so wild it blows my mind every time 🤯🤯🤯 And they actually made it happen for Riemannian 3-folds 🤯🤯🤯

粘性項を含むNavier-Stokes方程式の定常解がチューリング完全性を有することを示したとする論文が出ました 流体力学における解析に一石を投じる論文です 過渡解や3次元リーマン多様体以外への拡張などはまだ課題ですが、非常に興味深い研究だと思います。

Thank you for the recommendation Eva Miranda ! Excited to read this

An extension of the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

Fluids That Compute• Navier-Stokes Cracked with Cosymplectic Geometry. Certain steady (unchanging over time) fluid flows, described by the Navier-Stokes equations, can act like a universal computer, capable of performing any calculation a computer can do. These flows occur on

Turing complete Navier-Stokes steady states via cosymplectic geometry • Astrophysics Data System ui.adsabs.harvard.edu/abs/2025arXiv2…

"Education isn't something you can finish." - Isaac Asimov (1920 - 1992)

Eva Miranda The harmonic 1-forms making a cameo in Navier-Stokes universes? That’s a plot twist I didn't see coming 🌀 Curious if the geometry nudges these solutions toward chaos or order—bet there’s more lurking beneath the cosymplectic hood.

"Without geometry, life is pointless" #mathjoke

My talk will be streamed at the BIMSA youtube chanel. youtube.com/live/EKHTSNo0T… The time of my talk is 9:40 Beijing time on Friday 18. After that, it will be uploaded on the official website of the conference.

This talk will be streamed at the BIMSA youtube chanel. youtube.com/live/EKHTSNo0T… The time of my talk is 9:40 Beijing time on Friday 18. After that, it will be uploaded on the official website of the conference.

【共対称幾何によるナビエ・ストークス方程式の定常解のチューリング完全性　簡易解説】 結論: ホッジ分解が許容される3次元リーマン多様体において、粘性項を持つナビエ・ストークス方程式の定常解はチューリング完全性を持つ形で構築できる。 1/6 ↓続く Eva Miranda arxiv.org/abs/2507.07696