All time C∞-regularity of the interface in degenerate diffusion: a geometric approach
2001; Duke University Press; Volume: 108; Issue: 2 Linguagem: Inglês
10.1215/s0012-7094-01-10824-7
ISSN1547-7398
AutoresP. Daskalopoulos, Robert Hamilton, Kwangjin Lee,
Tópico(s)Navier-Stokes equation solutions
ResumoWe study the connection between the geometry and all time regularity of the interface in degenerated diffusion. Our model considers the porous medium equation ut=Δum, m>1, with initial data u0 nonnegative, integrable, and compactly supported. We show that if the initial pressure f0=u0m− is smooth up to the interface and in addition it is root-concave and also satisfies the nondegeneracy condition |Df0|≠0 at $\partial\overline {\rm supp}$f0, then the pressure fm−1 remains C∞-smooth up to the interface and root-concave, for all time $0 < t < ∞$. In particular, the free boundary is C∞-smooth for all time.
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