Publications (14)
Global existence and limiting behavior of unidirectional flocks for the fractional Euler Alignment system
Daniel Lear
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels for $α\i…
Time-periodic non-radial solutions near monotone vortices in linearized 2D Euler
Ãngel Castro, Daniel Lear
We study the linearized 2D Euler equations around radial vortex profiles. Previous works have shown that the strict monotonicity of the vorticity profile leads to axisymmetrization…
Time periodic solutions for the 2D Euler equation near Taylor-Couette flow
Ãngel Castro, Daniel Lear
In this paper we consider the incompressible 2D Euler equation in an annular domain with non-penetration boundary condition. In this setting, we prove the existence of a family of…
Unidirectional flocks in hydrodynamic Euler Alignment system II: Singular models
Daniel Lear, Roman Shvydkoy
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels for $α\i…
On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating
Anna Abbatiello, Miroslav Bulicek, Daniel Lear
We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier pro…
Traveling waves near Poiseuille flow for the 2D Euler equation
Ãngel Castro, Daniel Lear
In this paper we reveal the existence of a large family of new, nontrivial and Lipschitz traveling waves for the 2D Euler equation at an arbitrarily small distance from the Poiseui…
Existence and stability of unidirectional flocks in hydrodynamic Euler Alignment systems
Daniel Lear, Roman Shvydkoy
In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel moti…
Global solutions to multi-dimensional topological Euler alignment systems
Daniel Lear, David N. Reynolds, Roman Shvydkoy
We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems e…
Grassmannian reduction of Cucker-Smale systems and dynamical opinion games
Daniel Lear, David N. Reynolds, Roman Shvydkoy
In this note we study a new class of alignment models with self-propulsion and Rayleigh-type friction forces, which describes the collective behavior of agents with individual char…
Global existence of quasi-stratified solutions for the confined IPM equation
Angel Castro, Diego Córdoba, Daniel Lear
In this paper, we consider a confined physical scenario to prove global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous…
Traveling waves near Couette flow for the 2D Euler equation
Ãngel Castro, Daniel Lear
In this paper we reveal the existence of a large family of new, nontrivial and smooth traveling waves for the 2D Euler equation at an arbitrarily small distance from the Couette fl…
On the non-diffusive Magneto-Geostrophic equation
Daniel Lear
Motivated by an equation arising in magnetohydrodynamics, we address the well-posedness theroy for the non-diffusive magneto-geostrophic equation. Namely, an active scalar equation…
Geometric Structure of Mass Concentration Sets for Pressureless Euler Alignment Systems
Daniel Lear, Trevor M. Leslie, Roman Shvydkoy +1
We study the limiting dynamics of the Euler Alignment system with a smooth, heavy-tailed interaction kernel and unidirectional velocity . We de…
On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term
Angel Castro, Diego Córdoba, Daniel Lear
We consider the 2D Boussinesq equations with a velocity damping term in a strip , with impermeable walls. In this physical scenario, where the \textit{Bouss…