Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces
Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces
In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mfenced open="‖" close="‖" separators="|"><mml:mrow><mml:mi>θ</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="script">X</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:math> vanishes at infinity.