caa a22 4500 463171098 CHVBK 20180406164813.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s00021-005-0193-3 doi (NATIONALLICENCE)springer-10.1007/s00021-005-0193-3 On the Local Smoothness of Solutions of the Navier-Stokes Equations [Elektronische Daten] [Hongjie Dong, Dapeng Du] Abstract.: We consider the Cauchy problem for incompressible Navier-Stokes equations $$u_t + u\nabla_xu - \Delta_xu + \nabla_xp = 0,\; {\text{div}}\,u = 0\;{\text{in}}\;\mathbb{R}^d \times \mathbb{R}^ +$$ with initial data in $$L^d (\mathbb{R}^d )$$ , and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have $$t^{m + n/2} D_t^m D_x^n u \in L^{d + 2} (\mathbb{R}^d \times (0,T))$$ , as long as $$||u||_{L_{x,t}^{d + 2} (R^d \times (0,T))}$$ stays finite. Birkhäuser Verlag, Basel, 2006 Navier-Stokes equations nationallicence regularity nationallicence mild solutions nationallicence Dong Hongjie University of Minnesota, 127 Vincent Hall, 55455, Minneapolis, MN, USA aut Du Dapeng University of Minnesota, 127 Vincent Hall, 55455, Minneapolis, MN, USA aut Journal of Mathematical Fluid Mechanics Birkhäuser-Verlag; www.birkhäuser.ch 9/2(2007-06-01), 139-152 1422-6928 9:2<139 2007 9 21 https://doi.org/10.1007/s00021-005-0193-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00021-005-0193-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dong Hongjie University of Minnesota, 127 Vincent Hall, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 700 1- Du Dapeng University of Minnesota, 127 Vincent Hall, 55455, Minneapolis, MN, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Fluid Mechanics Birkhäuser-Verlag; www.birkhäuser.ch 9/2(2007-06-01), 139-152 1422-6928 9:2<139 2007 9 21 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer