Lecture Notes on Intermittent Weak Solutions of the Three-dimensional Navier-Stokes Equations

This summary closely follows the paper Buckmaster et al. (Wild solutions of the Navier-Stokes equations whose singular sets in time have hausdorff dimension strictly less than 1, 2018. ArXiv:1809.00600) by the authors, which contains all the details regarding the specific gluing and convex integration technique used here. The lectures will be supplemented with material from the recent review paper Buckmaster and Vicol (EMS Surv. Math. Sci. 6(1/2):173–263, 2019), which contains the necessary background concerning weak solutions of the Euler and Navier-Stokes equations, their connection to phenomenological theories of fully developed turbulence, and the convex integration methods used to construct them.