Steady flow with unilateral and leak/slip boundary conditions by the Stokes variational–hemivariational inequality

ABSTRACT

The stationary Stokes equations for a generalized Newtonian fluid with nonlinear unilateral, and slip and leak boundary conditions are investigated. Boundary conditions include the generalized Clarke gradient and the convex subdifferential, and the variational formulation of the problem is the variational–hemivariational inequality for the velocity field. Existence and uniqueness result for weak solution is proved by using a surjectivity theorem for a pseudomonotone perturbation of a maximal monotone operator.

Keywords:

• Stokes equation
• generalized Newtonian fluid
• unilateral boundary condition
• slip
• leak
• frictional boundary condition

2010 Mathematics Subject Classifications:

• 35Q35
• 47J20
• 49J40
• 76D07
• 35M86

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The project is supported by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 CONMECH, by Natural Science Foundation of Guangxi Grant No: 2018GXNSFAA281353, and by the Beibu Gulf University under project No. 2018KYQD06. The first author is also supported by the projects financed by the Ministry of Science and Higher Education of Republic of Poland under Grants Nos. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019.