Work Plan for the Study of non-Smooth Solutions in 3D Fluid Dynamics: The First Regularity Barrier for the Euler Equation

The hope of finding solutions of the fluid dynamic equations developing anomalous behaviors starting from smooth data has stimulated the search for increasingly sophisticated configurations. I too want to add my contribution in these pages, by proposing the construction of possible candidates and experimenting with some numerical schemes. The tests are carried out for the Euler case in a very simple situation, however they may open the way to more complex cases in fluid dynamics, including Navier-Stokes equations. If the intuition is correct, it should not be difficult for those more skilled in theoretical matters to bring home some more concrete mathematical results.