# American Institute of Mathematical Sciences

March  2011, 10(2): 653-665. doi: 10.3934/cpaa.2011.10.653

## Global wellposedness for a transport equation with super-critial dissipation

 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received  May 2010 Revised  October 2010 Published  December 2010

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 Holder spaces.
Citation: Xumin Gu. Global wellposedness for a transport equation with super-critial dissipation. Communications on Pure & Applied Analysis, 2011, 10 (2) : 653-665. doi: 10.3934/cpaa.2011.10.653
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