Ja n 20 01 Scalars convected by a 2 D incompressible flow
نویسندگان
چکیده
1 Abstract We provide a test for numerical simulations, for several two dimensional incompressible flows, that appear to develop sharp fronts. We show that in order to have a front the velocity has to have uncontrolled velocity growth. The aim of this paper is to study the possible formation of sharp fronts in finite time for a scalar convected by a two dimensional divergence-free velocity field, with x = (x 1 , x 2) ∈ R 2 or R 2 /Z 2 , and t ∈ [0, T) with T ≤ ∞. The * Partially supported by NSF grant DMS 0070692.
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