96-188 Jiahong Wu

Inviscid Limits and Regularity Estimates for the Solutions of 2-D Dissipative Quasi-geostrophic Equations (24K, latex) May 10, 96

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We discuss two important topics of turbulence theory: inviscid limit and decay of Fourier spectrum for the 2-D dissipative quasi-geostrophic (QGS) equations. In the first part we consider inviscid limits for both smooth and weak solutions of the 2-D dissipative QGS equations and prove that the classical solutions with smooth initial data tend to the solutions of the corresponding non-dissipative equations as the dissipative coefficient tends to zero. Here the convergence is in the strong $L^2$ sense and we give the optimal convergence rate. For the weak solutions of the dissipative QGS equations with $L^2$ initial data, we obtain weak $L^2$ inviscid limit result. In the second part we use the methods of Foias-Temam \cite{FT} and Doering-Titi \cite{DT} developed for the Navier-Stokes equations to establish exponential decay of spatial Fourier spectrum for the solutions of the dissipative QGS equations, but we treat general norms and our method of estimating the nonlinear terms are different. \end{abstract}

Files: 96-188.src( desc , 96-188.txt )