Strong convergence of the vorticity and conservation of the energy for the α-Euler equations
Strong convergence of the vorticity and conservation of the energy for the α-Euler equations
Abstract In this paper, we study the convergence of solutions of the α -Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity ω 0 in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>x</mml:mi> <mml:mi>p</mml:mi> </mml:msubsup> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>p</mml:mi> <mml:mo>∈</mml:mo> <mml:mo …