A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows(http://www.math.psu.edu/bressan/PSPDF/prize1.pdf) and blocking problems(http://www.math.psu.edu/bressan/PSPDF/prize2.pdf)..
The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011.

