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- W2899360023 abstract "Direct linkages from the isometric embeddings of Riemannian manifolds to the compressible fluid dynamics are established. More precisely, let $(M,g)$ be a surface isometrically embedded in $mathbb{R}^3$; by defining the density $rho$, velocity $v$ and pressure $p$ in terms of the second fundamental form of the embedding, we get a solution for the steady compressible Euler equations of fluid dynamics. We also introduce a renormalization process to obtain solutions for Euler equations from non-$C^2$ isometric embeddings of the flat torus. Extensions to multi-dimensions are discussed." @default.
- W2899360023 created "2018-11-09" @default.
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- W2899360023 date "2018-11-05" @default.
- W2899360023 modified "2023-09-27" @default.
- W2899360023 title "From the Nash--Kuiper Theorem to the Euler Equations of Fluid Dynamics" @default.
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