11 papers
Hypothetical Singularity of 3D Navier-Stokes in Clay Institute set up Reduces to Axisymmetric with Swirl class
Rishad Shahmurov
We prove a singular-endpoint reduction for the three-dimensional incompressible Navier--Stokes large-data regularity problem in the smooth finite-energy class. The result is a redu…
Global Regularity for Axisymmetric Navier--Stokes Flows with Swirl
Rishad Shahmurov
We prove global smoothness for smooth finite-energy axisymmetric solutions of the three-dimensional incompressible Navier--Stokes equations with arbitrary swirl. The proof is organ…
A Classical Two-Part First-Threshold Proof of Global Smoothness for Navier--Stokes: Axisymmetric Swirl Closure and Full-System Reduction
Rishad Shahmurov
We prove global smooth continuation for smooth finite-energy solutions of the three-dimensional incompressible Navier--Stokes equations by a two-part first-threshold argument. Part…
Large-Data Global Regularity for Three-Dimensional Navier--Stokes I: A Direct First-Threshold Continuation Proof for the Axisymmetric Swirl Class
Rishad Shahmurov
This is the first paper in a two-part direct-threshold series on large-data global regularity for the three-dimensional Navier--Stokes equations. We prove a direct first-threshold…
Euler Singularities II: Interior Quadrupole Blow-Up for Smooth Axisymmetric Euler with Swirl in \texorpdfstring{}
Rishad Shahmurov
We present a self-contained interior quadrupole mechanism for finite-time singularity formation in the axisymmetric three-dimensional incompressible Euler equations with swirl in t…
Euler Singularities I: Boundary Blow-Up for Smooth Exact-Odd Axisymmetric Euler with Swirl
Rishad Shahmurov
We construct smooth axisymmetric-with-swirl initial data in a periodic cylinder for which the three-dimensional incompressible Euler evolution develops a finite-time boundary singu…