p-Euler equations and p-Navier–Stokes equations


Journal Article

© 2017 Elsevier Inc. We propose in this work new systems of equations which we call p-Euler equations and p-Navier–Stokes equations. p-Euler equations are derived as the Euler–Lagrange equations for the action represented by the Benamou–Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the ‘momentum’ is the signed (p−1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier–Stokes equations. If γ=p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier–Stokes equations in Rd for γ=p and p≥d≥2 through a compactness criterion.

Full Text

Duke Authors

Cited Authors

  • Li, L; Liu, JG

Published Date

  • April 5, 2018

Published In

Volume / Issue

  • 264 / 7

Start / End Page

  • 4707 - 4748

Electronic International Standard Serial Number (EISSN)

  • 1090-2732

International Standard Serial Number (ISSN)

  • 0022-0396

Digital Object Identifier (DOI)

  • 10.1016/j.jde.2017.12.023

Citation Source

  • Scopus