Regularity Criteria for the Velocity Field of Three‐Dimensional Shear‐Thinning Fluids in the Framework of Besov Spaces

This paper investigates the regularity criteria for the velocity field of three‐dimensional shear‐thinning fluids in the framework of Besov spaces. We obtain that when the specific negative exponent of the velocity field satisfies certain integrability conditions in Besov space, its regularity can be completely characterized by a set of parameter constraints. This research breaks through the limitations of the traditional Sobolev space theory and provides a new mathematical tool for describing the flow of non‐Newtonian fluid with rough characteristics. In addition, the results not only improve the existing theoretical results but also lay a strict mathematical foundation for the dynamic behavior analysis of complex fluids under nonsmooth conditions.