Transition to thermohydrodynamic lubrication problem

0474369 - MÚ 2018 RIV US eng J - Journal Article
Ciuperca, I. S. - Feireisl, Eduard - Jai, M. - Petrov, A.
Transition to thermohydrodynamic lubrication problem.
Quarterly of Applied Mathematics. Roč. 75, č. 3 (2017), s. 391-414. ISSN 0033-569X. E-ISSN 1552-4485
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : free boundary problems * lubrication * asymptotic approach * Stokes equation
OECD category: Pure mathematics
Impact factor: 0.853, year: 2017
http://www.ams.org/journals/qam/2017-75-03/S0033-569X-2017-01468-X/

We consider a non-isothermal Stokes equation used to calculate the pressure distribution in a thin layer of lubricant film between two surfaces. The problem is described in 2D and 3D settings by the Stokes and heat transfer equations. Under appropriate regularity assumptions on the data, existence results for the non-isothermal Stokes is recalled. Using a formal asymptotic expansion, we obtain a generalized Reynolds equation coupled with a limit energy equation, the so-called non-isothermal Reynolds system. Then existence and uniqueness are proved for this system by using a fixed-point argument. Finally, a rigorous justification of the convergence is established.
Permanent Link: http://hdl.handle.net/11104/0271438