On anisotropic energy conservation criteria of incompressible fluids

2025/09/10 by Yanqing Wang, Wang, Yanqing, Wei, Wei +2
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.08348

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by means of divergence-free condition, we establish an anisotropic energy conservation class enabling one component of velocity in the largest space L³ (0,T; B^1/3_3,∞) for the 3D inviscid incompressible fluids, which extends the celebrated result obtained by Cheskidov, Constantin, Friedlander and Shvydkoy in [15, Nonlinearity 21 (2008)]. For viscous flows, we generalize famous Lions's energy conservation criteria to allow the horizontal components and vertical part of velocity to have different integrability.

Citations

• Energy conservation for 3D Euler and Navier-Stokes equations in a bounded domain. Applications to Beltrami flows
• On the energy and helicity conservation of the incompressible Euler equations
• Three results on the Energy conservation for the 3D Euler equations
• Energy conservation for weak solutions of incompressible fluid equations: the Hölder case and connections with Onsager's conjecture
• On the Shinbrot's criteria for energy equality to Newtonian fluids: A simplified proof, and an extension of the range of application
• Remarks on the energy equality for the non-Newtonian fluids
• Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws
• On the energy equality for solutions to Newtonian and non-Newtonian fluids
• Energy equality for the Navier-Stokes equations in weak-in-time Onsager\n spaces
• Onsager's energy conservation for inhomogeneous Euler equations
• A Proof of Onsager's Conjecture
• On the interior regularity criteria of the 3-D Navier-Stokes equations involving two velocity components
• On the critical one component regularity for 3-D Navier-Stokes system
• Dissipative Euler Flows and Onsager's Conjecture
• Statistical hydrodynamics

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• Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum