8 citations · 34 across the 14 of their papers we have counts for
14 papers
Non-uniqueness of global-in-time admissible weak solutions to the isentropic compressible Euler equations for a dense set of initial data
Daniel W. Boutros, Simon Markfelder
In recent years, the technique of convex integration has demonstrated that for some initial data (also referred to as 'wild initial data'), many PDE models of mathematical fluid me…
A Generalized Framework for Convex Integration and its Application to Geophysical Models
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
In this paper a general framework for convex integration is developed, in order to construct weak solutions to the Cauchy problem, by building on ideas from [C. De Lellis and L. Sz…
A mathematical study of an elastic-viscous-plastic sea-ice model with the Kelvin-Voigt rheology
Daniel W. Boutros, Xin Liu, Marita Thomas +1
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical…
Regularity thresholds for anomalous dissipation and related phenomena in passive scalars
Marco Bagnara, Daniel W. Boutros, Camillo De Lellis +1
We prove the absence of anomalous dissipation for passive scalars driven by some random autonomous divergence-free vector fields in . In dimension we just need c…
The global attractor of the Toner-Tu-Swift-Hohenberg equations of active turbulence and its properties
Daniel W. Boutros, Kolluru Venkata Kiran, John D. Gibbon +1
The Toner-Tu-Swift-Hohenberg (TTSH) equations are one of the basic equations that are used to model turbulent behaviour in active matter, specifically the swarming of bacteria in s…
On the absence of anomalous dissipation for the Navier-Stokes equations with Navier boundary conditions: a sufficient condition
Claude Bardos, Daniel W. Boutros, Edriss S. Titi
We consider the three-dimensional incompressible Navier-Stokes equations in a bounded domain with Navier boundary conditions. We provide a sufficient condition for the absence of a…
Global well-posedness of the elastic-viscous-plastic sea-ice model with the inviscid Voigt-regularisation
Daniel W. Boutros, Xin Liu, Marita Thomas +1
In this paper, we initiate the rigorous mathematical analysis of the elastic-viscous-plastic (EVP) sea-ice model, which was introduced in [E. C. Hunke and J. K. Dukowicz, J. Phys.…
On the removal of the barotropic condition in helicity studies of the compressible Euler and ideal compressible MHD equations
Daniel W. Boutros, John D. Gibbon
The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting the conse…
On the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations
Daniel W. Boutros, Edriss S. Titi
Classical solutions of the three-dimensional Euler equations of an ideal incompressible fluid conserve the helicity. We introduce a new weak formulation of the vorticity formulatio…
Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and a…
Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains
Claude Bardos, Daniel W. Boutros, Edriss S. Titi
We consider the three-dimensional incompressible Euler equations on a bounded domain with boundary. We prove that if the velocity field with (w…
Phase transitions in the fractional three-dimensional Navier-Stokes equations
Daniel W. Boutros, John D. Gibbon
The fractional Navier-Stokes equations on a periodic domain differ from their conventional counterpart by the replacement of the Laplacian term by $ν_…
On Energy Conservation for the Hydrostatic Euler Equations: An Onsager Conjecture
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
Onsager's conjecture, which relates the conservation of energy to the regularity of weak solutions of the Euler equations, was completely resolved in recent years. In this work, we…
Onsager's Conjecture for Subgrid Scale -Models of Turbulence
Daniel W. Boutros, Edriss S. Titi
The first half of Onsager's conjecture states that the Euler equations of an ideal incompressible fluid conserve energy if with $θ> \frac…