On the Local Type I Conditions for the 3D Euler Equations
We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution v ∈ L ∞ ( - 1 , 0 ; L 2 ( B ( x 0 , r ) ) ) ∩ L loc ∞ ( - 1 , 0 ; W 1 , ∞ ( B ( x 0 , r ) ) ) of the 3D Euler equations, where B ( x 0 , r ) is the...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2018-11, Vol.230 (2), p.641-663 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution
v
∈
L
∞
(
-
1
,
0
;
L
2
(
B
(
x
0
,
r
)
)
)
∩
L
loc
∞
(
-
1
,
0
;
W
1
,
∞
(
B
(
x
0
,
r
)
)
)
of the 3D Euler equations, where
B
(
x
0
,
r
)
is the ball with radius
r
and the center at
x
0
, if the limiting values of certain scale invariant quantities for a solution
v
(·,
t
) as
t
→
0
are small enough, then
∇
v
(
·
,
t
)
does not blow-up at
t
= 0 in
B
(
x
0
,
r
). |
|---|---|
| ISSN: | 0003-9527 1432-0673 |
| DOI: | 10.1007/s00205-018-1254-0 |