64 citations · 308 across the 37 of their papers we have counts for
42 papers
On Leonardo da Vinci's paradox
Björn Gebhard, Lukas Niebel, Christian Seis
Buoyancy points straight upward, yet in the absence of external forces, a rising air bubble may trace a spiral through the water. This phenomenon was already observed by Leonardo d…
Long-time behavior of optimal mixing in an advection-diffusion shell model
Jiajia Guo, Baole Wen, Christian Seis +1
We investigate the long-time behavior of optimal mixing in an advection-diffusion equation using a shell model framework. Our focus is on quantifying the decay of the scalar varian…
Non-Existence of thick bubble rings at low Weber numbers
Yuanjiang Han, Christian Seis
We examine the existence of thick bubble rings within the framework of the free-boundary capillary Euler equations, focusing on the regime of low Weber numbers. Although spheroidal…
Steady bubbles and drops in inviscid fluids
David Meyer, Lukas Niebel, Christian Seis
We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a b…
Exponential mixing by random cellular flows
Víctor Navarro-Fernández, Christian Seis
We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the pas…
Steady Ring-Shaped Vortex Sheets
David Meyer, Christian Seis
In this work, we construct traveling wave solutions to the two-phase Euler equations, featuring a vortex sheet at the interface between the two phases. The inner phase exhibits a u…
Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain
Christian Seis, Emil Wiedemann, Jakub Woźnicki
In the vanishing viscosity limit from the Navier-Stokes to Euler equations on domains with boundaries, a main difficulty comes from the mismatch of boundary conditions and, consequ…
Optimal Regularity for the 2D Euler Equations in the Yudovich class
Nicola de Nitti, David Meyer, Christian Seis
We analyze the optimal regularity that is exactly propagated by a transport equation driven by a velocity field with BMO gradient. As an application, we study the 2D Euler equation…
Stability of traveling waves for doubly nonlinear equations
Christian Seis, Dominik Winkler
In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave so…
Fine large-time asymptotics for the axisymmetric Navier--Stokes equations
Christian Seis, Dominik Winkler
We examine the large-time behavior of axisymmetric solutions without swirl of the Navier--Stokes equation in . We construct higher-order asymptotic expansions for the…
Finite-dimensional leading order dynamics for the fast diffusion equation near extinction
Beomjun Choi, Christian Seis
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant mani…
Optimal regularity of isoperimetric sets with Hölder densities
Lisa Beck, Eleonora Cinti, Christian Seis
We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild (-)Hölder regularity assumptions on the density functions. Our main…
Invariant Manifolds for the Thin Film Equation
Christian Seis, Dominik Winkler
The large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on is examined: We investigate the higher order as…
Propagation of regularity for transport equations. A Littlewood-Paley approach
David Meyer, Christian Seis
It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can…
On the dynamics of vortices in viscous 2D flows
Stefano Ceci, Christian Seis
We study the 2D Navier--Stokes solution starting from an initial vorticity mildly concentrated near distinct points in the plane. We prove quantitative estimates on the propaga…
Asymptotics near extinction for nonlinear fast diffusion on a bounded domain
Beomjun Choi, Robert J. McCann, Christian Seis
On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected…
On the dynamics of point vortices for the 2D Euler equation with vorticity
Stefano Ceci, Christian Seis
We study the evolution of solutions to the 2D Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumptio…
Optimal stability estimates and a new uniqueness result for advection-diffusion equations
Víctor Navarro-Fernández, André Schlichting, Christian Seis
This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev reg…
A well-posedness result for a system of cross-diffusion equations
Christian Seis, Dominik Winkler
This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, un…
On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity
Helena J. Nussenzveig Lopes, Christian Seis, Emil Wiedemann
We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the i…
The Scharfetter--Gummel scheme for aggregation-diffusion equations
André Schlichting, Christian Seis
In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme…
Bounds on the rate of enhanced dissipation
Christian Seis
We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper…
A note on the vanishing viscosity limit in the Yudovich class
Christian Seis
We consider the inviscid limit for the two-dimensional Navier--Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between…
Vortex dynamics for 2D Euler flows with unbounded vorticity
Stefano Ceci, Christian Seis
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described b…