60 citations · 730 across the 55 of their papers we have counts for
33 papers · 1 filter
Distance Geometry and a Hydrodynamical Hopf-Rinow Criterion
Theodore D. Drivas, Patrick Heslin, Gerard Misiołek
The hydrodynamical Hopf-Rinow problem asks whether a given reconfiguration of an ideal fluid can be attained by an Euler flow. On the flat two-dimensional torus, we give an equival…
Geometry of strong forces in continuum mechanics
Theodore D. Drivas, Daniil Glukhovskiy
Consider a material point in finite dimensions moving under the influence of a potential force according to Newton's laws. Suppose the potential energy function is a generalized we…
On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Theodore D. Drivas, Tarek M. Elgindi, Daniel Ginsberg
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in…
Lagrangian aspects of Yudovich theory for 2D Euler
Theodore D. Drivas, Joonhyun La
In this note, we establish Yudovich's existence and uniqueness result for bounded (as well as mildly unbounded) vorticity weak solution of the two-dimensional incompressible Euler…
On the fragility of laminar flow
Theodore D. Drivas, Daniel Ginsberg, Marc Nualart
Inviscid laminar flow is a stationary solution of the incompressible Euler equations whose streamlines foliate the fluid domain. Their structure on symmetric domains is rigid: all…
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 geometric characterization of steady laminar flow
Theodore D. Drivas, Marc Nualart
We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non-contractible streamlines which…
The Feynman-Lagerstrom criterion for boundary layers
Theodore D. Drivas, Sameer Iyer, Trinh T. Nguyen
We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor…
Islands in stable fluid equilibria
Theodore D. Drivas, Daniel Ginsberg
We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric periodic channels must posses "islands", or cat's eye vortices. In this way, arbitrarily…
Twisting in Hamiltonian Flows and Perfect Fluids
Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting…
On the Support of Anomalous Dissipation Measures
Luigi De Rosa, Theodore D. Drivas, Marco Inversi
By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solut…
On the distribution of heat in fibered magnetic fields
Theodore D. Drivas, Daniel Ginsberg, Hezekiah Grayer
We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (in…
On maximally mixed equilibria of two-dimensional perfect fluids
Michele Dolce, Theodore D. Drivas
The vorticity of a two-dimensional perfect (incompressible and inviscid) fluid is transported by its area preserving flow. Given an initial vorticity distribution , predicting…
Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids
Theodore D. Drivas, Tarek M. Elgindi, Joonhyun La
We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure o…
Singularity formation in the incompressible Euler equation in finite and infinite time
Theodore D. Drivas, Tarek M. Elgindi
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattere…
Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries
Theodore D. Drivas, Huy Q. Nguyen, Camilla Nobili
We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies wi…
Flexibility and rigidity of free boundary MHD equilibria
Peter Constantin, Theodore D. Drivas, Daniel Ginsberg
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that…
Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data
Tristan Buckmaster, Theodore D. Drivas, Steve Shkoller +1
A fundamental question in fluid dynamics concerns the formation of discontinuous shock waves from smooth initial data. We prove that from smooth initial data, smooth solutions to t…
Conjugate and cut points in ideal fluid motion
Theodore D. Drivas, Gerard Misiołek, Bin Shi +1
Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be se…
On quasisymmetric plasma equilibria sustained by small force
Peter Constantin, Theodore D. Drivas, Daniel Ginsberg
We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equ…
Flexibility and rigidity in steady fluid motion
Peter Constantin, Theodore D. Drivas, Daniel Ginsberg
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouvil…
A stochastic approach to enhanced diffusion
Michele Coti Zelati, Theodore D. Drivas
We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are Hölder regular or Lipschitz continuous with critical points…
Anomalous Dissipation in Passive Scalar Transport
Theodore D. Drivas, Tarek M. Elgindi, Gautam Iyer +1
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible $C^\infty([0,T)\times \mathbb{T}^d)\cap L^1(…
Inviscid limit of vorticity distributions in Yudovich class
Peter Constantin, Theodore D. Drivas, Tarek M. Elgindi
We prove that given initial data , forcing , and any , the solutions of Navier-Stokes converge…