On Nonstationary Stokes Problem and Navier–Stokes Problem in a Half-Space with Initial Data Nondecreasing at Infinity
By V. Solonnikov. 2003
106 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/326f76cdff2cfee2fdae0a17975892b55838d1fa
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In Applied Mathematics
- Ken Abe
- Jürgen Saal
- Yoshikazu Giga
- Matthias Hieber
- Yoshihiro Shibata
- Senjo Shimizu
- T. Iwabuchi
- Ryo Takada
In Computational Theory and Mathematics
Citations in the corpus
- The L∞-Stokes semigroup in exterior domains (2012, background): “So far, L∞-type theory has been only established when = Rn [25] (see also [27,42]) and Rn + [5,50].”
- The Fujita–Kato approach to the Navier–Stokes equations in the rotational framework (2010, background): “More precisely, these authors prove local existence of mild solutions to the problem (1.1) for initial data u0 belonging to L ∞a (R 3 ), a suitable subspace of L ∞ (R 3 ). For a different approach also in the context of local solutions, we also refer to [ 16 ].”
- Analyticity of the Stokes semigroup in spaces of bounded functions (2011, background): “Then instead of using conventional parabolic local Hölder estimate, we are forced to use Schauder estimates for the Stokes equations and Helmholtz decomposition for Hölder spaces developed by V. A. Solonnikov [58] since the boundary value problem for the Stokes equations cannot be reduced to usual”
- The stokes equation in the Lp-setting: Well-posedness and regularity properties (2018, background): “Note, however, that Solonnikov proved in [194] also estimates for the solution u of the Stokes equation in spaces of bounded functions.”
- Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, background): “When Ω = R+, the analyticity of the semigroup is known in L∞-type spaces including C0,σ(Ω), the L∞-closure of C∞ c,σ(Ω), the space of all smooth solenoidal vector fields compactly supported in Ω [11] (see also [38, 28]).”