From the Nash--Kuiper Theorem to the Euler Equations of Fluid Dynamics
Li, Siran ; Slemrod, Marshall
arXiv, 1811.01505 / Harvested from arXiv
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.
Publié le : 2018-11-04
Classification:  Mathematics - Analysis of PDEs,  Physics - Fluid Dynamics
@article{1811.01505,
     author = {Li, Siran and Slemrod, Marshall},
     title = {From the Nash--Kuiper Theorem to the Euler Equations of Fluid Dynamics},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1811.01505}
}
Li, Siran; Slemrod, Marshall. From the Nash--Kuiper Theorem to the Euler Equations of Fluid Dynamics. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1811.01505/