#A note about the derivation of the Navier-Stokes equations and it is written when I was taking the reading course with Prof. David Hoff in Indiana University. [[pdf/Derivation-NSE.pdf|Download]] #The following notes are aiming to understand the famous paper titled" Well-posedness for the Navier-Stokes equations" by H. Koch and D. Tataru. Download [[pdf/Koch-Tataru-NSE-1.pdf|Note 1]], [[pdf/Koch-Tataru-NSE-2.pdf|Note 2]], [[pdf/Koch-Tataru-NSE-2.pdf|Note 3]] and see also [[post/196|Leray projection - NSE Notes I]], [[post/197|Kernel estimates I - NSE notes II]], [[post/198|Kernel estimates II - NSE notes II]], [[post/199|A pointwise estimate - NSE notes V]], [[post/200|the invariance of BMO^{-1}-norm - NSE notes III]], [[post/201|Fixed point theorem - NSE notes IV]]