# [M1 Seminar II] Week 3 : Regularities of the Solution

This week we will prove that the solution of the system $u$ is in $C^0([0,T], W^{s,2}) \cap C^1([0,T], W^{s-1,2})$ so that $u \in C_b^1 ([0,T] \times \Bbb R^n)$. For this purpose we first show that $u \in L^\infty ([0,T], W^{s,2})$, … Continue reading