Global existence for 3D non-stationary Stokes flows with Coulomb’s type friction boundary conditions

References

• Richardson S. On the no-slip boundary condition. J Fluid Mech. 1973;59:707–719.
   Web of Science ®Google Scholar
• Bucur D, Feireisl E, Necasova S. Influence of wall roughness on the slip behaviour of viscous fluids. Proc Roy Soc Edinburgh Sect A. 2008;138:957–973.
   Google Scholar
• Bucur D, Feireisl E, Necasova S. On the asymptotic limit of flows past a ribbed boundary. J Math Fluid Mech. 2008;10(4):554–568.
   Web of Science ®Google Scholar
• Bucur D, Feireisl E, Necasova S, et al. On the asymptotic limit of the Navier--Stokes system on domains with rough boundaries. J Differ Equ. 2008;244(11):2890–2908.
   Web of Science ®Google Scholar
• Brezina J. Asymptotic properties of solutions to the equations of incompressible fluid mechanics. J Math Fluid Mech. 2010;12:536–553.
   Web of Science ®Google Scholar
• Barrat J, Bocquet L. Large slip effect at a nonwetting fluid-solid interface. Phys Rev Lett. 1999;820(23):4671–4674.
   Web of Science ®Google Scholar
• Baudry J, Charlaix E, Tonck A, et al. Experimental evidence for a large slip effect at a nonwetting fluid-solid interface. Langmuir. 2001;17(17):5232–5236.
   Web of Science ®Google Scholar
• Tretheway D, Meinhart C. Apparent fluid slip at hydrophobic microchannel walls. Phys Fluids. 2002;14:L9.
   Web of Science ®Google Scholar
• Zhu Y, Granick S. No-slip boundary condition switches to partial slip when fluid contains surfactant. Langmuir. 2002;18(26):10058–10063.
   Web of Science ®Google Scholar
• Hervet H, Léger L. Flow with slip at the wall: from simple to complex fluids. C R Acad Sci Paris Phys. 2003;4:241–249.
   Web of Science ®Google Scholar
• Navier C. Mémoire sur les lois du mouvement des fluides. Mém Acad Royal Soc. 1823;6:389–416.
   Google Scholar
• Bonaccurso E, Butt H, Craig V. Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system. Phys Rev Lett. 2003;90(14):144501.
   PubMed Web of Science ®Google Scholar
• Zhu Y, Granick S. Limits of the hydrodynamic no-slip boundary condition. Phys Rev Lett. 2002;88(10):106102.
   PubMed Web of Science ®Google Scholar
• Magnin A, Piau JM. Shear rheometry of fluids with a yield stress. J Non-Newtonian Fluid Mech. 1987;23:91–106.
   Web of Science ®Google Scholar
• Ionescu IR, Sofonea M. The blocking property in the study of Bingham fluids. Int J Eng Sci. 1986;24(3):289–297.
   Web of Science ®Google Scholar
• Fujita H. Flow problems with unilateral boundary conditions. Leçons: Collège de France; 1993.
   Google Scholar
• Fujita H. A mathematical analysis of motions of viscous incompressible fluid under leak or slip boundary conditions. Math Fluid Mech Model. 1994;888:199–216.
   Google Scholar
• Fujita H. A coherent analysis of Stokes flows under boundary conditions of friction type. J Comput Appl Math. 2002;149:57–69.
   Web of Science ®Google Scholar
• Saito N. On the Stokes equations with the leak and slip boundary conditions of friction type: regularity of solutions. Publ RIMS Kyoto Univ. 2004;40:345–383.
   Web of Science ®Google Scholar
• Haslinger J, Stebel J, Sassi T. Shape optimization for Stokes problem with threshold slip. Appl Math. 2014;59(6):631–652.
   Web of Science ®Google Scholar
• Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
   Google Scholar
• Duvaut G. Équilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb. C R Acad Sci Paris. 1980;t 290:263–265.
   Google Scholar
• Fujita H. Non-stationary Stokes flows under leak boundary conditions of friction type. J Comput Math. 2001;19:1–8.
   Web of Science ®Google Scholar
• Saito N, Fujita H. Regularity of solutions to the Stokes equation under a certain nonlinear boundary condition. The Navier--Stokes equations. Lecture Note Pure Appl Math. 2001;223:73–86.
   Google Scholar
• Li Y, Li K. Global strong solution of two dimensional Navier--Stokes equations with nonlinear slip boundary conditions. J Math Anal Appl. 2012;393(1):1–13.
   Web of Science ®Google Scholar
• Kashiwabara T. On a strong solution of the non-stationary Navier--Stokes equations under slip or leak boundary conditions of friction type. J Differ Equ. 2013;254(2):756–778.
   Web of Science ®Google Scholar
• Coulomb CA. Théorie des machines simples. Paris: Bachelier; 1821.
   Google Scholar
• Kondrat’ev VA, Oleinik OA. Boundary-value problems for the system of elasticity theory in unbounded domains. Korn’s inequailities. Russian Math Surv. 1988;43(5):65–119.
   Web of Science ®Google Scholar
• Duvaut G. Loi de frottement non locale. Indian J. Pure Appl. Math. 1982;13(8):73–78.
   Google Scholar
• Demkowicz L, Oden JT. On some existence and uniqueness results in contact problems with nonlocal friction. Nonlinear Anal TMA. 1982;6(10):1075–1093.
   Web of Science ®Google Scholar
• Consiglieri L. Existence for a class of non-Newtonian fluids with a nonlocal friction boundary condition. Acta Math Sin Eng Ser. 2006;22(2):523–534.
   Web of Science ®Google Scholar
• Sofonea M, Farcas A. Analysis of a history-dependent frictional contact problem. Appl Anal. 2014;93(2):428–444.
   Web of Science ®Google Scholar
• Temam R. Navier--Stokes equations. Amsterdam: North-Holland; 1984.
   Google Scholar
• Coddington EA, Levinson N. Theory of ordinary differential equations. New York (NY): Mc Graw-Hill; 1955.
   Google Scholar
• Girault V, Raviart PA. Finite element approximation of the Navier--Stokes equations. Berlin: Springer-Verlag; 1979.
   Google Scholar
• Roubicek T. Nonlinear partial differential equations with applications. Basel: Birkhauser-Verlag; 2005.
   Google Scholar
• Monteiro Marques M. Differential inclusions in non-smooth mechanical problems: shocks and dry friction. Boston: Birkhauser; 1993.
   Google Scholar
• Boukrouche M, Boussetouan I, Paoli L. Non-isotermal Navier--Stokes system with mixed boundary conditions and friction law: uniqueness and regularity properties. Nonlinear Anal TMA. 2014;102:168–185.
   Web of Science ®Google Scholar