Global well-posedness in variable exponent Besov-Morrey spaces for the fractional porous medium equation

This paper is concerned with the study of the fractional porous medium equation in variable exponent Besov-Morrey spaces. In the case 1 < ? ? 2, by using the Chemin mono-norm method, we prove global well-posedness for small initial data in the critical variable exponent Besov-Morrey spaces ?N 2?2m??+d/q(?) r(?),q(?),h (Rd) with 1??/2 < m < 1 + d/2q(?), 0 < ? < ? ? 1, 1 ? r(?) ? q(?) < ? and 1 ? h ? ?. In the limit case ? = 1, we establish the global well-posedness for small initial data in ?N 1?2m+ d/q(?) r(?),q(?),1 (Rd) with 1/2 < m < 1 + d/q(?) and 1 ? r(?) ? q(?) < ?.