A Remark on the Global Well-posedness of the 2D Generealized SQG
 发布时间： 2017-04-19     13:15   【返回上一页】 发布人：酒全森

北京师范大学数学科学学院

/begin{eqnarray*}

&&/omega_t+u/cdot/nabla/omega=0, x/in R^2, t>0,//[3mm]
&& u=K/ast/omega,

/end{eqnarray*}

with $K(x)=/frac{x^/perp}{|x|^{2+2/alpha}},0/le/alpha/le/frac12.$ When $/alpha=0$, it is the two-dimensional Euler equations.  When $/alpha=/frac 12$, it corresponds to SQG. We will prove that if the existence interval of the smooth solution to SQG is $[0,T]$, then when $/alpha</frac 12$ the existence interval of the generalized SQG will keep on $[0,T]$.