Local existence and uniqueness in the largest critical space for a surface growth model

Details Local existence and uniqueness in the largest critical space for a surface growth model Local existence and uniqueness in the largest critical space for a surface growth model

2010-03-22

arxiv.org/abs/1003.4298v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to scaling and we prove our results in the largest possible critical space such that weak solutions are defined. The uniqueness of global weak solutions remains unfortunately open, unless the initial conditions are sufficiently small.

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