A non-local inequality and global existence

作者：Gressman Philip T; Krieger Joachim; Strain Robert M^*

来源：Advances in Mathematics, 2012, 230(2): 642-648.

DOI：10.1016/j.aim.2012.02.017

• Kinetic theory
• Landau equation
• Model equation
• Global regularity

In this article we prove a collection of new non-linear and non-local integral inequalities. As an example for u >= 0 and p is an element of (0, infinity) we obtain
integral(R3) dx u(p+1)(x) <= (p+1/p)(2) integral(R3) dx {(-Delta)(-1) u(x)} vertical bar del u(p/2) (x)vertical bar(2).
We use these inequalities to deduce global existence of solutions to a non-local heat equation with a quadratic non-linearity for large radial monotonic positive initial conditions. Specifically, we improve Krieger and Strain (in press) [4] to include all alpha is an element of (0, 74/75).

• 出版日期2012-6-1