Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation

2025/07/14 by Kamal N. Soltanov, Soltanov, Kamal N.
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2507.10094

Abstract

This article examines the smoothness of the solution to the Navier-Stokes equation from a novel perspective. Here, the existence of the smoother solution relative to x and to the time t was shown only for a finite time. Moreover, for each considered case of the problem, a blowup time for its solutions can be demonstrated.

Citations

• On the integrability properties of Leray-Hopf solutions of the Navier-Stokes equations on ℝ³
• Remarks on the uniqueness of weak solutions of the incompressible Navier-Stokes equations
• Partial regularity of Solutions of Navier-Stokes equations
• Finite time blowup for an averaged three-dimensional Navier-Stokes equation

Related

• The Navier-Stokes equations for Incompressible Flows: solution properties at potential blow-up times
• Finite time blow up for a model of incompressible Navier-Stokes Equations
• Finite-time blowup for smooth solutions of the Navier--Stokes equations on the whole space with linear growth at infinity
• Dynamical Behavior for the Solutions of the Navier-Stokes Equation
• Well-posedness, Smoothness and Blow-up for Incompressible Navier-Stokes Equations