### 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 Ẇ
^{1}
q-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 W
^{1}
q-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 |
---|---|

Article number | 1950004 |

Journal | Bulletin of Mathematical Sciences |

Volume | 9 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 Apr 1 |

### Fingerprint

### Keywords

- Boundary value problem
- Measurable coefficients
- Stokes systems

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**
L
_{q}
-estimates for stationary stokes system with coefficients measurable in one direction
.** / Dong, Hongjie; Kim, Doyoon.

Research output: Contribution to journal › Article

_{q}-estimates for stationary stokes system with coefficients measurable in one direction ',

*Bulletin of Mathematical Sciences*, vol. 9, no. 1, 1950004. https://doi.org/10.1142/S1664360719500048

}

TY - JOUR

T1 - L q -estimates for stationary stokes system with coefficients measurable in one direction

AU - Dong, Hongjie

AU - Kim, Doyoon

PY - 2019/4/1

Y1 - 2019/4/1

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 Ẇ 1 q-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 W 1 q-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 Ẇ 1 q-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 W 1 q-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=85065607278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065607278&partnerID=8YFLogxK

U2 - 10.1142/S1664360719500048

DO - 10.1142/S1664360719500048

M3 - Article

AN - SCOPUS:85065607278

VL - 9

JO - Bulletin of Mathematical Sciences

JF - Bulletin of Mathematical Sciences

SN - 1664-3607

IS - 1

M1 - 1950004

ER -