3 citations · 4 across the 5 of their papers we have counts for
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On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations
G. Seregin, V. Sverak
Local regularity of axially symmetric solutions to the Navier-Stokes equations is studied. It is shown that under certain natural assumptions there are no singularities of Type I.
On the large-distance asymptotics of steady state solutions of the Navier-Stokes equations in 3D exterior domains
Alexander Korolev, Vladimir Sverak
We identify the leading term describing the behavior at large distances of the steady state solutions of the Navier-Stokes equations in 3D exterior domains with vanishing velocity…
Liouville theorems for the Navier-Stokes equations and applications
G. Koch, N. Nadirashvili, G. Seregin +1
We study bounded ancient solutions of the Navier-Stokes equations. These are the solutions which are defined for all past time. In two space dimensions we prove that such solutions…
Zeros of complex caloric functions and singularities of complex viscous Burgers equation
Peter Polacik, Vladimir Sverak
We show that the 1d viscous Burgers equation considered for complex valued functions develops finite-time singularities from compactly supported smooth data. By means of the Cole-H…
On self-similar singular solutions of the complex Ginzburg-Landau equation
Petr Plechac, Vladimir Sverak
We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe…