Abstract
AbstractThe two-dimensional Stokes IBVP on $$(0,T)\times \Omega $$
(
0
,
T
)
×
Ω
is investigated under the assumptions that $$\Omega \subset {\mathbb {R}}^2$$
Ω
⊂
R
2
is a smooth exterior domain, the initial datum $$v_0$$
v
0
belongs to $$L^\infty (\Omega )$$
L
∞
(
Ω
)
and $$(v_0,\nabla \phi )=0$$
(
v
0
,
∇
ϕ
)
=
0
for all $$\phi \in L^1_{\ell oc}(\Omega )$$
ϕ
∈
L
ℓ
o
c
1
(
Ω
)
with $$\nabla \phi \in L^1(\Omega )$$
∇
ϕ
∈
L
1
(
Ω
)
. The well-posedeness in $$L^\infty ((0,T)\times \Omega )$$
L
∞
(
(
0
,
T
)
×
Ω
)
and the maximum modulus theorem are achieved, in particular one deduces that the Stokes semigroup on $$L^\infty (\Omega )$$
L
∞
(
Ω
)
is a bounded analytic semigroup.
Funder
Università degli Studi della Campania Luigi Vanvitelli
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics