4 papers · 1 filter
Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory
Philip Isett, Yuchen Mao, Sung-Jin Oh +1
We introduce a new versatile method for constructing solution operators (i.e., right-inverses up to a finite rank operator) for a wide class of underdetermined PDEs , whic…
Intermittency and Dissipation Regularity in Turbulence
Luigi De Rosa, Theodore D. Drivas, Marco Inversi +1
We lay down a geometric-analytic framework to capture properties of energy dissipation within weak solutions to the incompressible Euler equations. For solutions with spatial Besov…
A proof of Onsager's Conjecture for the SQG equation
Philip Isett, Shi-Zhuo Looi
We construct solutions to the SQG equation that fail to conserve the Hamiltonian while having the maximal allowable regularity for this property to hold. This result solves the gen…
On the conservation laws and the structure of the nonlinearity for SQG and its generalizations
Philip Isett, Andrew Ma
Using a new definition for the nonlinear term, we prove that all weak solutions to the SQG equation (and mSQG) conserve the angular momentum. This result is new for the weak soluti…