K. M. Adeyemo and E. O. Ayoola, Profile decomposition and singularity formation in the critical Brinkman–Forchheimer equation, Eur. J. Math. Appl. 6 (2026), Article ID 6.
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Volume 6 (2026), Article ID 6
https://doi.org/10.28919/ejma.2026.6.6
Published: 31/07/2026
Abstract:
The Brinkman–Forchheimer equation describes viscous flow through porous media with nonlinear drag. In three dimensions, the profile-decomposition $\dot H^{1/2}(\mathbb{R}^3)$ is the natural setting for concentration phenomena because it is invariant under the Navier–Stokes scaling. This paper develops a profile-decomposition framework for the critical Brinkman–Forchheimer equation in order to distinguish regular initial data from singularity-generating initial data. The analysis combines linear profile decomposition, nonlinear perturbation theory, compactness–rigidity arguments, energy estimates, and blow-up criteria. The main outcomes are: a precise decomposition of bounded critical sequences, a stability theorem for nonlinear profiles, global regularity under smallness or strong damping assumptions, and singularity criteria showing that any blow-up must be carried by a nontrivial concentrated profile.
How to Cite:
K. M. Adeyemo and E. O. Ayoola, Profile decomposition and singularity formation in the critical Brinkman–Forchheimer equation, Eur. J. Math. Appl. 6 (2026), Article ID 6. https://doi.org/10.28919/ejma.2026.6.6