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This presentation will discuss recent advancements in the regularity of the three-dimensional incompressible Navier–Stokes equation, a system of partial differential equations that describes the behavior of fluids. While the full regularity of the 3D incompressible Navier–Stokes equation remains an open question, there have been substantial breakthroughs within the fluid dynamics community. In this talk, I will present several a priori interior and boundary trace estimates, which extend and refine the current understanding of higher derivative estimates in mixed norms. Subsequently, we will explore the applications in the inviscid limit problem, which investigates the limiting behavior as viscosity approaches zero, considering both characteristic and noncharacteristic boundary conditions.

Reception at 3:45pm