PDE Seminar Mathematical study on the spin-coating-process

2007-04-16 16:30 - 2007-04-16 17:30
Faculty of Science Building #8 Room 309
Okihiro Sawada (Hokkaido Univ.)
We consider the motion of viscous flow on a rotating disc,which illustrates the spin-coating-process.To avoid the difficulty of contact angle problem(in particular, complicated boundary conditions),the domain is essentially like the infinity layer.The motion of liquid is discribed by the Navier-Stokesequations with Coriolis, and centrifugal-force terms.The Navier's slip boundary conditon is imposed atthe bottom of the liquid, which is determined bythe altitude of liquid.The motion of the surface of the liquid is determinedby the balance of the surface-tension, motion of theliquid on the surface and the evaporation effect.The purpose is to establish the time-local existenceof the solutions to the linearized problem, using themaximal regularity theory.The key idea to the proof is to apply the method ofNewton polygon.