TY - JOUR
T1 - Solvability for Stokes System in Hölder Spaces in Bounded domains and Its Applications
AU - Chang, Tongkeun
AU - Kang, Kyungkeun
N1 - Publisher Copyright:
© 2018, Springer Nature Switzerland AG.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We consider Stokes system in bounded convex domains and we present conditions of given data, in particular, boundary data, which ensure Hölder continuity of solutions. For Hölder continuous solutions for the Stokes system the normal component of boundary data requires a bit more regular than boundary data of Hölder continuous solutions for the heat equation. We also construct an example, which shows that Hölder continuity is no longer valid, unless the proposed condition of boundary data is fulfilled. As an application, we consider a certain general types of nonlinear systems coupled to fluid equations and local well-posedness is established in Hölder spaces.
AB - We consider Stokes system in bounded convex domains and we present conditions of given data, in particular, boundary data, which ensure Hölder continuity of solutions. For Hölder continuous solutions for the Stokes system the normal component of boundary data requires a bit more regular than boundary data of Hölder continuous solutions for the heat equation. We also construct an example, which shows that Hölder continuity is no longer valid, unless the proposed condition of boundary data is fulfilled. As an application, we consider a certain general types of nonlinear systems coupled to fluid equations and local well-posedness is established in Hölder spaces.
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U2 - 10.1007/s00021-018-0392-3
DO - 10.1007/s00021-018-0392-3
M3 - Article
AN - SCOPUS:85056792395
VL - 20
SP - 1857
EP - 1888
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 4
ER -