64 citations · 308 across the 37 of their papers we have counts for
4 papers · 2 filters
Optimal stability estimates for continuity equations
Christian Seis
This review paper is concerned with the stability analysis of the continuity equation in the DiPerna--Lions setting in which the advecting velocity field is Sobolev regular. Quanti…
Convergence rates for upwind schemes with rough coefficients
André Schlichting, Christian Seis
This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where th…
On the vortex filament conjecture for Euler flows
Robert L. Jerrard, Christian Seis
In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in $\mathb…
A quantitative theory for the continuity equation
Christian Seis
In this work, we provide stability estimates for the continuity equation with Sobolev vector fields. The results are inferred from contraction estimates for certain logarithmic Kan…