An alternative energy bound derivation for a generalized Hasegawa-Mima equation

作者：Bronski Jared C; Fetecau Razvan C^*

来源：Nonlinear Analysis: Real World Applications , 2012, 13(3): 1362-1368.

DOI：10.1016/j.nonrwa.2011.10.012

• Kuramoto-Sivashinsky equation
• Global attractors
• Dissipative dynamics

We present an alternative derivation of the H-1-boundedness of solutions to a generalized Hasegawa-Mima equation, first investigated by Grauer (1998) [2]. We apply a Lyapunov function technique similar to the one used for constructing energy bounds for the Kuramoto-Sivashinsky equation. Different from Grauer (1998) [2], who uses this technique in a Fourier space approach, we employ the physical space construction of the Lyapunov function, as developed in Bronski and Gambill (2006) [11]. Our approach has the advantage that it is more transparent in what concerns the estimates and the dominant terms that are being retained. A key tool of the present work, which replaces the algebraic manipulations on the Fourier coefficients from the other approach, is a Hardy-Rellich type inequality.

• 出版日期2012-6