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math.AP2026
On Global-in-time Solutions of Incompressible MHD Equations with Small Alfvén Numbers
Fei Jiang, Xiao Ren, Yi Zhou
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfvén number, will reduce the nonlinear interaction and inhibit the for…
math.AP2026
Forward self-similar solutions to the 2D Navier--Stokes equations
Dallas Albritton, Julien Guillod, Mikhail Korobkov +1
We construct self-similar solutions to the 2D Navier--Stokes equations evolving from arbitrarily large --homogeneous initial data and present numerical evidence for their non-u…
math.AP2024
On basic velocity estimates for the plane steady-state Navier-Stokes system and its applications
Mikhail Korobkov, Xiao Ren
We consider some new estimates for general steady Navier-Stokes solutions in plane domains. According to our main result, if the domain is convex, then the difference between mean…