What about compressible fluids? Existing Navier-Stokes models for compressible fluids:

"On the implosion of a compressible fluid II: Singularity formation" (2022) https://projecteuclid.org/journals/annals-of-mathematics/vol...

"Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2

...

From https://news.ycombinator.com/item?id=49389524#49404787:

> "I/Q Sampling for Signal Phase" (2026-08) https://share.gemini.google/rDVcVwDnWPTc :

>> It's a Twistor-Grassmanian mapping?

From "Navier-Stokes Breakthrough, FTLE, and SQG" (2026-09) https://share.gemini.google/sq2XmhphMFWE :

> The Mathematical Formulation: Because SQS is explicitly a superfluid Bose–Einstein condensate, treating it purely as a classical Navier–Stokes fluid misses quantized vorticity. The full formulation maps to the Gross–Pitaevskii (Euler–Korteweg) equations via the Madelung transformation

...

> To adapt the Córdoba–Martínez-Zoroa (CMZ) / Buckmaster / OpenAI Lean cascade to Euler–Korteweg, three core structural adjustments must be made:

> - Irrotationality Constraint

> - Third-Order Dispersion

> - Hydrodynamic Energy Functional