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Convex integration for a class of active scalar equations. (English) Zbl 1231.35177
The main objective of this paper is to explore the extent to which the method of convex integration applies to the construction of wild weak solutions to the general class of active scalar equations. The discussion employs the use of persistent oscillatory waves. It is shown that the solutions may have Fourier support in a narrow cone region.

MSC:
35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B10 Periodic solutions to PDEs
35D30 Weak solutions to PDEs
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