Abstract
AbstractThe paper is concerned with the IBVP in exterior domains of the two-dimensional Stokes equations. The goal was to investigate the well-posedness in the set of solutions assuming an initial data $$u_0\in L^\infty (\Omega )$$
u
0
∈
L
∞
(
Ω
)
, divergence free, and enjoying the property "Equation missing" for all $$t>0$$
t
>
0
and c independent of u. For all $$u_0\in L^\infty $$
u
0
∈
L
∞
, divergence-free one shows examples of non-uniqueness in the above set of solutions.
Funder
Università degli Studi della Campania Luigi Vanvitelli
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
Reference28 articles.
1. Abe K., Exterior Navier-Stokes flows for bounded data, Math. Nachr. 290 (2017) 972–985. https://doi.org/10.1002/mana.201600132.
2. Abe K., On the large time$$L^\infty $$-estimates of the Stokes semigroup in two dimensional exterior domains, arXiv:1912.01193v1.
3. Abe K. and Giga Y., The$$L^\infty $$-Stokes semigroup in exterior domains, J. Evol. Equ., 14 (2014), no. 1, 1–28.
4. Abe K. and Giga Y., Analyticity of the Stokes semigroup in spaces of bounded functions, Acta Math. 211 (2013), no. 1, 1–46.
5. Abe K., Giga Y. and Hieber M., Stokes resolvent estimates in spaces of bounded functions, Ann. Sci. Éc. Norm. Supér. 48 (2015) 537–559.
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