The paper gives sharp spectral gap conditions for existence of inertial manifolds for abstract semilinear parabolic equations with non-self-adjoint leading part. Main attention is paid to the case where this leading part have Jordan cells which appear after applying the so-called Kwak transform to various important equations such as 2D Navier–Stokes equations, reaction-diffusion-advection systems, etc. The different forms of Kwak transforms and relations between them are also discussed.

中文翻译：

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重新审视了Kwak变换和惯性流形

给出了具有非自伴前导部分的抽象半线性抛物方程的惯性流形存在的尖锐的谱隙条件。主要注意以下情况：该前导部分具有约旦单元，这些单元在将所谓的Kwak变换应用于各种重要方程（例如2D Navier–Stokes方程，反应扩散对流系统等）之后出现。Kwak的不同形式还讨论了它们之间的变换和关系。