Global Regulatory for 3D Navier-Stokes Equation via Two Case Energy Decay Analysis : small data

Key Points

• The aim is to establish global regularity for the three-dimensional Navier-Stokes equations with large initial data.
• Uses unconditional energy decay to prove global regularity.
• Applies the Beale-Kato-Majda criterion to show uniform boundedness of vorticity.
• Focuses on divergence-free initial conditions in H¹(ℝ³).
• Proves a unique global smooth solution exists for any divergence-free initial condition.
• Demonstrates that vorticity remains uniformly bounded, preventing blowup.
• Resolves the large data scenario of a millennium prize problem.