2025/05/22 by Taichi Eguchi, T. Eguchi · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical mechanics #Compressibility #Energy (signal processing) #Inviscid flow #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Stability and Controllability of Differential Equations #Statistics
paper · pdf · doi:10.1007/s00208-025-03189-4
published in Mathematische Annalen 392(3), 4105-4121 (Springer Nature)
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
Abstract We find a new criterion for the validity of the energy equality of the 3D fractional Navier–Stokes equations in the framework of the Lorentz–Besov spaces. Note that our sufficient condition is strictly weaker than that of Cheskidov et al. (Nonlinearity 21:1233–1252, 2008) related to the largest class L3(0,T;B1/33,∞ ) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>;</mml:mo> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for the validity of the energy conservation law of the Euler equations. Moreover, taking the inviscid limit of the fractional Navier–Stokes equations, we obtain the energy conservation law of the Euler equations in the framework of the same Lorentz–Besov spaces. Our result covers the recent work of Cheskidov and Luo (Nonlinearity 33:1388–1403, 2020) for the Navier–Stokes equations. Furthermore, we mention the relation between our new criterion and the Onsager conjecture.