Hexagonal structures in 2D flows - NASI, Matheus Carneiro Leão (2025)
On the paper Hexagonal Structures in 2D Navier-Stokes Flows, [Bra22], by Lorenzo Bran- dolese, the author studies the sponteneous formation of hexagonal structures in 2D flows of Leray’s solutions to the Navier-Stokes equations. The author also analyzes the isotropic character of the energy density in two-dimensional fluids in the far field, showing that the particles are nowhere at rest at large distances. In this dissertation, we go through the cal- culations and results obtained by the author in detail. Moreover, we extend some results to the more general MHD system, and show a necessary condition on the estimate for the lower bound of the far field radius (found in [BV07]) so that such hexagonal structures appear.