TY - JOUR
T1 - Lq -estimates for stationary Stokes system with coefficients measurable in one direction
AU - Dong, Hongjie
AU - Kim, Doyoon
N1 - Publisher Copyright:
© 2018, The Author(s).
PY - 2018
Y1 - 2018
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
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 -