• Corpus ID: 231925376

Optimal stability estimates and a new uniqueness result for advection-diffusion equations

@inproceedings{NavarroFernandez2021OptimalSE,
  title={Optimal stability estimates and a new uniqueness result for advection-diffusion equations},
  author={V'ictor Navarro-Fern'andez and Andr{\'e} Schlichting and Christian Seis},
  year={2021}
}
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 regular in the spatial variable. This estimate is formulated with the help of Kantorovich–Rubinstein distances with logarithmic cost functions. Second, the stability estimates are extended to the advection-diffusion equations with velocity fields whose gradients are singular integrals of L functions entailing a new well… 
View PDF on arXiv
1 Citations
Background Citations
1
Methods Citations
1

One Citation

Citation Type

Citation Type

Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients
We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are…

References

SHOWING 1-10 OF 40 REFERENCES
Ordinary differential equations, transport theory and Sobolev spaces
SummaryWe obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on…
Lagrangian flows for vector fields with gradient given by a singular integral
We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an L1 function. Such estimates allow to prove existence,…
Estimates and regularity results for the DiPerna-Lions flow
Abstract In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple…
Topics in optimal transportation, vol. 58 of Graduate Studies in Mathematics
  • American Mathematical Society,
  • 2003
Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L1 Vorticity
TLDR
This paper addresses a question that arose in \cite{FilhoMazzucatoNussenzveig06}, namely whether 2D Euler solutions obtained via vanishing viscosity are renormalized when the initial data has low integrability.
Optimal stability estimates for continuity equations
  • Christian Seis
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2018
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. Quantitative estimates for…
A quantitative theory for the continuity equation
Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients
We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are…
Advection Diffusion Equations with Sobolev Velocity Field
In this note we study advection diffusion equations associated to incompressible $W^{1,p}$ velocity fields with $p>2$. We present new estimates on the energy dissipation rate and we discuss…
Bounds on the rate of enhanced dissipation
  • Preprint arXiv:2003.08794
  • 2020
...
1
2
3
4
...