It is well-known that if $u \in L^2_{t,x}(B_1 \times (-1,0))$ is a solution of heat equation, then heat equation is smooth in $B_{1/2}\times (-1/4,0)$. However, it is not true for nonstationary Stokes and Navier-Stokes equations. In this expository talk, we first study a classical theory of Navier-Stokes equations that does not consider an effect of pressure. Next, by introducing suitable weak solutions, we control pressures by using harmonic analysis techniques such as div-curl lemmas and paraproduct decompositions. These estimates help us to get a regularity of solutions of Navier-Stokes equations.