Symmetry and Blow-Up for 3D Modified CBF Equations in Sobolev–Gevrey Spaces

We study the three-dimensional modified critical homogeneous convective Brinkman–Forchheimer equations. Local existence and uniqueness are obtained via the Fixed Point Theorem, and under the assumption of finite maximal existence time, we establish blow-up criteria in Sobolev–Gevrey spaces. The model preserves Euclidean invariances (translations and rotations) and, when α=0, the critical scaling symmetry of the 3D Navier-Stokes system. The blow-up thresholds are shown to depend mainly on the Gevrey structure rather than on any loss of symmetry.