Infinite lifetime for the starlike dynamics in Hele-Shaw cells

• One of the folklore questions in the theory of free boundary problems is the lifetime of the starlike dynamics in a Hele-Shaw cell. We prove precisely that, starting with a starlike analytic phase domain Omega(0), the Hele-Shaw chain of subordinating domains Omega( t), Omega(0) = Omega(0), exists for an infinite time under injection at the point of starlikeness.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

free boundary problem

Hele-Shaw flow

univalent function

starlike function

Lowner-Kufarev equation

moving boundary-problem

flows

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