I'm reading Majda's book, on page 110, I cannot understand how to get $v\in C_W (0,T;H^{m})$ from the above.
And he wrote "$[\phi,v^{\epsilon}]\to[\phi,v]$ uniformly on $[0,T]$ " two times, do the two bracketssquare brackets have the same meaning? Which is the dual pair on $H^{m}$ or $H^{m^{'}}$? I'm really comfused.
Any suggestions are welcome! Thank all of you!