CPAA
Global wellposedness for a transport equation with super-critial dissipation
Xumin Gu
Communications on Pure & Applied Analysis 2011, 10(2): 653-665 doi: 10.3934/cpaa.2011.10.653
We study a one-dimensional transport equation with non-local velocity and supercritial dissipation. Using the methods of modulus of continuity introduced in [1] and fractional Laplacian representaiton introduced in [2], we prove its global well-posedness for small periodic initial data in Holder spaces.
keywords: global regularity. Super-critical dissipation modulus of continuity fractional Laplacian

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