Weighted Gagliardo-Nirenberg inequalities involving BMO norms and solvability of strongly coupled parabolic systems (Q2789502)

New weighted Gagliardo-Nirenberg inequalities are introduced together with applications to the local/global existence of solutions to nonlinear strongly coupled and uniform parabolic systems of the form NEWLINE\[NEWLINE u_t=\operatorname{div}A(x,t,u,Du)+ f(x,t,u,Du),\quad (x,t)\in Q.NEWLINE\]NEWLINE Much weaker sufficient conditions than those existing in the literature for the solvability of these systems are established.