Abstract
The authors construct self-similar solutions for an N-dimensional transport equation, where the velocity is given by the Riezs transform. These solutions imply nonuniqueness of weak solution. In addition, self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.
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Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday
Project supported by the MCINN (Spain) (No. MTM2008-03754) and the ERC (No. StG-203138CDSIF).
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Castro, A., Córdoba, D. Self-similar solutions for a transport equation with non-local flux. Chin. Ann. Math. Ser. B 30, 505–512 (2009). https://doi.org/10.1007/s11401-009-0180-8
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DOI: https://doi.org/10.1007/s11401-009-0180-8