The generalized Constantin–Lax–Majda (gCLM) equation was introduced to model the competing effects of advection and vortex stretching in hydrodynamics. Recent investigations revealed possible connections with the two-dimensional turbulence. With this connection in mind, we consider the steady problem for the viscous gCLM equations on ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn1.gif] {$\mathbb{T}$} : ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn2.gif] {$av{\omega }_{x}-{v}_{x}\omega =\nu {\Delta}\omega +f,v={\left(-{\Delta}\right)}^{-\frac{1}{2}}\omega ,$} where ##IMG## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn3.gif] {$a\in \mathbb{R}$} is the parameter measuring the relative strength between advection and stretching, ν > 0 is the viscosity constant, and f is a given O (1)-forcing independent of ν . For some range of param...

中文翻译：

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关于带O（1）强迫的广义Constantin-Lax-Majda方程的平稳解和无粘性极限

引入了通用的康斯坦丁-拉克斯-马伊达方程（gCLM），以模拟流体动力学中对流和涡旋拉伸的竞争效应。最近的研究表明可能与二维湍流有关。考虑到这种联系，我们考虑## IMG ## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn1.gif]上粘性gCLM方程的稳定问题$ \ mathbb {T} $}：## IMG ## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn2.gif] {$ av {\ omega} _ { x}-{v} _ {x} \ omega = \ nu {\ Delta} \ omega + f，v = {\ left（-{\ Delta} \ right）} ^ {-\ frac {1} {2} } \ omega，$}，其中## IMG ## [http://ej.iop.org/images/0951-7715/33/12/6662/nonaba93eieqn3.gif] {$ a \ in \ mathbb {R} $ }是测量对流和拉伸之间相对强度的参数，ν> 0是粘度常数，并且f是一个独立于ν的给定的O（1）强迫。对于某些参数范围...