Diff. Geom, Math. Phys., PDE Seminar: Sung-Jin Oh

In this talk, we will describe a construction of compactly supported solutions to the three-dimensional incompressible Euler equations on $R \times R^3$ with Hölder regularity $1/5 -\epsilon$ in space and time. This work extends the earlier works of De Lellis-Székelyhidi, Buckmaster-De Lellis-Székelyhidi and Isett on construction of Hölder continuous dissipative Euler flows to the non-periodic setting. Our key technical innovation is a simple method for finding a compactly supported symmetric 2-tensor with a prescribed divergence, which obeys useful bounds.