A remark on vorticity maximal function

作者：Zhu Xiangrong

来源：Journal of Mathematical Analysis and Applications, 2008, 340(2): 1027-1032.

DOI：10.1016/j.jmaa.2007.09.024

• Euler equation
• vorticity
• BMO

In this note the following inequality is proved. For any nonnegative measure mu is an element of H-1 (R-2), x is an element of R-2 and 0 < r < 1, there holds
mu(B(x, r)) <= C(ln 1/r)(-1/2) parallel to mu parallel to(-1)(H)
where C is a positive constant. Using (1) an estimate for the vorticity maximal function similar to the estimate in Majda [A. Majda, Remarks on weak solutions for vortex sheets with a distinguished sign, Indiana Univ. Math. J. 42 (1993) 921-939] is established without assuming the initial vorticity having compact support. From this a more simple proof of the Delort's celebrated theorem [J.M. Delort, Existence de mappes de fourbillon en dimension deux, J. Amer. Math. Soc. 4 (1991) 553-586] is presented.

• 出版日期2008-4-15