Anomalous Dissipation in Passive Scalar Transport

speaker: Gautam Iyer (Carnegie Mellon University)

abstract: In this talk we study anomalous dissipation for passively transported scalars. The main result produces an explicit example of a bounded velocity field which is $C^\infty( 0, T) \times \mathbb{T}^d )$ and also $L^1( [0, T; C^{1-}( \mathbb{T}^d ) )$ for which the passively advected scalar exhibits anomalous dissipation. As a result we also obtain a simple example of non-uniqueness of transport equations for velocity fields in this class.

Our proof provides an criterion that guarantees anomalous dissipation provided the solutions of the associated inviscid equation grow so that the $H^2$ norm is bounded by the square of the $H^1$ norm. This is joint work with T. Drivas, T. Elgindi and I-J Jeong.

timetable:
Mon 24 Jan, 17:10 - 18:00,
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