2017/06/18 by Lei Li, Jian-Guo Liu, Li, Lei +2 · 1 citation
Mathematics · Physics and Astronomy · #35Q35 #49K30 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35Q35 #msc:49K30 #msc:76D03
paper · pdf · doi:10.48550/arxiv.1706.05693
openalex publication_date 2017/06/18 · arxiv created 2017/12/25 · arxiv updated 2017/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \it 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.