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The initial boundary-value problem (IBVP) and the Cauchy problem for theKuramoto--Sivashinsky equation and other related $2m$th-order semilinearparabolic partial differential equations in one and N dimensions areconsidered. Global existence and blow-up as well as uniform bounds are reviewedby using: (i) classic tools of interpolation theory and Galerkin methods, (ii)eigenfunction and nonlinear capacity methods, (iii) Henry's version of weightedGronwall's inequalities, and (vi) two types of scaling (blow-up) arguments. Forthe IBVPs, existence of global solutions is proved for both Dirichlet and"Navier" boundary conditions. For some related higher-order PDEs in Ndimensions uniform boundedness of global solutions of the Cauchy problem areestablished. As another related application, the well-posed Burnett-typeequations, which are a higher-order extension of the classic Navier-Stokesequations, are studied. As a simple illustration, a generalization of thefamous Leray-Prodi-Serrin-Ladyzhenskaya regularity results is obtained.

On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations