In this paper, we study the convergence of solutions of the alpha-Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity omega(0 )in L-x(p) for p is an element of (1,infinity), we prove strong convergence in L-t infinity L-x(p) of the vorticities q alpha , solutions of the alpha-Euler equations, towards a Lagrangian and energy-conserving solution of the Euler equations. Furthermore, if we consider solutions with bounded initial vorticity, we prove a quantitative rate of convergence of q(alpha) to omega in L-p , for p is an element of (1,infinity).

Strong convergence of the vorticity and conservation of the energy for the α-Euler equations

Spirito, Stefano
2024-01-01

Abstract

In this paper, we study the convergence of solutions of the alpha-Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity omega(0 )in L-x(p) for p is an element of (1,infinity), we prove strong convergence in L-t infinity L-x(p) of the vorticities q alpha , solutions of the alpha-Euler equations, towards a Lagrangian and energy-conserving solution of the Euler equations. Furthermore, if we consider solutions with bounded initial vorticity, we prove a quantitative rate of convergence of q(alpha) to omega in L-p , for p is an element of (1,infinity).
File in questo prodotto:
File Dimensione Formato  
Abbate_2024_Nonlinearity_37_035012.pdf

accesso aperto

Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 568.37 kB
Formato Adobe PDF
568.37 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/230163
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact