Abstract
We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori W˙q1-estimates for any q∈ [2 , ∞) when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a Wq1-estimate and prove the solvability for any q∈ (1 , ∞) when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
| Original language | English |
|---|---|
| Journal | Bulletin of Mathematical Sciences |
| DOIs | |
| Publication status | Accepted/In press - 2018 Jan 1 |
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Keywords
- Boundary value problem
- Measurable coefficients
- Stokes systems
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Lq -estimates for stationary Stokes system with coefficients measurable in one direction. / Dong, Hongjie; Kim, Doyoon.
In: Bulletin of Mathematical Sciences, 01.01.2018.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Lq -estimates for stationary Stokes system with coefficients measurable in one direction
AU - Dong, Hongjie
AU - Kim, Doyoon
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori W˙q1-estimates for any q∈ [2 , ∞) when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a Wq1-estimate and prove the solvability for any q∈ (1 , ∞) when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
AB - We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori W˙q1-estimates for any q∈ [2 , ∞) when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a Wq1-estimate and prove the solvability for any q∈ (1 , ∞) when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
KW - Boundary value problem
KW - Measurable coefficients
KW - Stokes systems
UR - http://www.scopus.com/inward/record.url?scp=85055260266&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85055260266&partnerID=8YFLogxK
U2 - 10.1007/s13373-018-0120-6
DO - 10.1007/s13373-018-0120-6
M3 - Article
AN - SCOPUS:85055260266
JO - Bulletin of Mathematical Sciences
JF - Bulletin of Mathematical Sciences
SN - 1664-3607
ER -