Math @ Duke

Publications [#333566] of JianGuo Liu
Papers Published
 Li, L; Liu, JG, pEuler equations and pNavier–Stokes equations,
Journal of Differential Equations, vol. 264 no. 7
(April, 2018),
pp. 47074748, Elsevier BV [doi]
(last updated on 2019/04/18)
Abstract: © 2017 Elsevier Inc. We propose in this work new systems of equations which we call pEuler equations and pNavier–Stokes equations. pEuler equations are derived as the Euler–Lagrange equations for the action represented by the Benamou–Brenier characterization of Wassersteinp distances, with incompressibility constraint. pEuler 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 pEuler equations have streamfunctionvorticity formulation, where the vorticity is given by the pLaplacian of the streamfunction. By adding diffusion presented by γLaplacian of the velocity, we obtain what we call pNavier–Stokes equations. If γ=p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a timeshift estimate, we show the global existence of weak solutions for the pNavier–Stokes equations in Rd for γ=p and p≥d≥2 through a compactness criterion.


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