Publications [#333566] of Jian-Guo Liu

Papers Published

1. Li, L; Liu, JG, p-Euler equations and p-Navier–Stokes equations, Journal of Differential Equations, vol. 264 no. 7 (April, 2018), pp. 4707-4748, Elsevier BV [doi]
   (last updated on 2025/02/21)

   Abstract:
   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.