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The primitive equations in the scaling-invariant space L∞(L1)
Consider the primitive equations on R 2 × ( z 0 , z 1 ) with initial data a of the form a = a 1 + a 2 , where a 1 ∈ BUC σ ( R 2 ; L 1 ( z 0 , z 1 ) ) and a 2 ∈ L σ ∞ ( R 2 ; L 1 ( z 0 , z 1 ) ) . These spaces are scaling-invariant and represent the anisotropic character of these equations. It is sho...
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| Published in: | Journal of evolution equations 2021-12, Vol.21 (4), p.4145-4169 |
|---|---|
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | Consider the primitive equations on
R
2
×
(
z
0
,
z
1
)
with initial data
a
of the form
a
=
a
1
+
a
2
, where
a
1
∈
BUC
σ
(
R
2
;
L
1
(
z
0
,
z
1
)
)
and
a
2
∈
L
σ
∞
(
R
2
;
L
1
(
z
0
,
z
1
)
)
. These spaces are scaling-invariant and represent the anisotropic character of these equations. It is shown that for
a
1
arbitrary large and
a
2
sufficiently small, this set of equations admits a unique strong solution which extends to a global one and is thus strongly globally well posed for these data provided
a
is periodic in the horizontal variables. The approach presented depends crucially on mapping properties of the hydrostatic Stokes semigroup in the
L
∞
(
L
1
)
-setting. It can be seen as the counterpart of the classical iteration schemes for the Navier–Stokes equations, now for the primitive equations in the
L
∞
(
L
1
)
-setting. |
|---|---|
| ISSN: | 1424-3199 1424-3202 |
| DOI: | 10.1007/s00028-021-00716-z |