30 citations · 71 across the 12 of their papers we have counts for
14 papers
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, Sam 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…
Intermittency and lower dimensional dissipation in incompressible fluids
Luigi De Rosa, Philip Isett
In the context of incompressible fluids, the observation that turbulent singular structures fail to be space filling is known as ``intermittency'' and it has strong experimental fo…
A direct approach to nonuniqueness and failure of compactness for the SQG equation
Philip Isett, Andrew Ma
We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [Buckmaster-Shkoller-Vicol, '16]. Our approach pro…
Nonuniqueness and existence of continuous, globally dissipative Euler flows
Philip Isett
We show that Hölder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples tha…
On the Endpoint Regularity in Onsager's Conjecture
Philip Isett
Onsager's conjecture states that the conservation of energy may fail for incompressible Euler flows with Hölder regularity below . This conjecture was recently solved by…
A Proof of Onsager's Conjecture
Philip Isett
For any , we construct weak solutions to the incompressible Euler equations in the class that have nonempty, compact support in time on ${\mathbb R} \times…
Holder Continuous Solutions of Active Scalar Equations
Philip Isett, Vlad Vicol
We consider active scalar equations , where is a divergence-free velocity field, and is a Fourier multiplier operator with s…
On Nonperiodic Euler Flows with Hölder Regularity
Philip Isett, Sung-Jin Oh
In [Isett,13], the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with Hölder regularity not exc…
A heat flow approach to Onsager's conjecture for the Euler equations on manifolds
Philip Isett, Sung-Jin Oh
We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of…
Regularity in time along the coarse scale flow for the incompressible Euler equations
Philip Isett
One of the most remarkable features of known nonstationary solutions to the incompressible Euler equations is the phenomenon known as the Taylor hypothesis, which predicts that coa…
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
Philip Isett
Building on the recent work of C. De Lellis and L. Székelyhidi, we construct global weak solutions to the three-dimensional incompressible Euler equations which are zero outside of…