In the paper, a new
slightly supercritical
condition, providing
local
regularity of axially symmetric solutions to the non-stationary 3D Navier-Stokes equations, is discussed. It generalises almost ...all known results in the local regularity theory of weak axisymmetric solutions.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In the note, a new regularity condition for axisymmetric solutions to the non-stationary 3D Navier–Stokes equations is proven. It is slightly supercritical.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier–Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier–Stokes ...equations have no Type I blowups.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this note, boundary Type I blowups of suitable weak solutions to the Navier–Stokes equations are discussed. In particular, it has been shown that, under certain assumptions, the existence of ...nontrivial mild bounded ancient solutions in half space leads to the existence of suitable weak solutions with Type I blowup on the boundary.
Full text
Available for:
DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Liouville type theorems for the stationary Navier-Stokes equations are proved under certain assumptions. These assumptions are motivated by conditions that appear in Liouville type theorems for the ...heat equations with a given divergence free drift.
A Liouville type theorem for mild bounded ancient solutions to the Navier-Stokes system in a half plane is proved, provided that a certain scale invariant quantity is bounded.
Full text
Available for:
DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $\Pi =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, subject to the slip ...boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(\Pi )$ satisfying the decay condition of the swirl component $ru^{\theta }_{0}\in L^{\infty }(\Pi )$.
Assuming that
T
is a potential blow up time for the Navier–Stokes system in
R
+
3
, we show that the norm of the velocity field in the Lorenz space
L
3
,
q
with
q
<
∞
goes to
∞
as time
t
approaches
T
....
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
PDF
