Regularity criterion for 3D Navier–Stokes equations in terms of the behavior of kinetic energy

Key Points

• The aim is to establish a regularity criterion for weak Leray–Hopf solutions of the Navier-Stokes equations based on kinetic energy.
• Analyzed the three-dimensional forced Navier–Stokes equations in a bounded domain.
• Developed theoretical proofs for regularity conditions.
• Constructed examples to demonstrate conditions where solutions remain regular.
• Proved that the weak Leray–Hopf solution is regular if kinetic energy is non-decreasing.
• Provided examples of solutions meeting the established regularity criteria.