## 6 Citations

The non-linear sewing lemma I: weak formulation

- Mathematics, Computer ScienceElectronic Journal of Probability
- 2019

It is proved that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique, and it is shown that under additional conditions of the approximation, there exists a unique Lipschitz flow.

The non-linear sewing lemma III: Stability and generic properties

- Mathematics
- 2020

Abstract Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme…

Constructing general rough differential equations through flow approximations

- MathematicsElectronic Journal of Probability
- 2022

The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated…

On the definition of a solution to a rough differential equation

- MathematicsAnnales de la Faculté des sciences de Toulouse : Mathématiques
- 2021

We give an elementary proof that Davie's definition of a solution to a rough differential equation and the notion of solution given by Bailleul in (Flows driven by rough paths) coincide. This…

Lorentz-equivariant flow with four delays of neutral type

- Physics
- 2021

We generalize electrodynamics with a second interaction in lightcone. The timereversible equations for two-body motion define a semiflow on C(R) with four state-dependent delays of neutral type and…

## References

SHOWING 1-10 OF 34 REFERENCES

The non-linear sewing lemma I: weak formulation

- Mathematics, Computer ScienceElectronic Journal of Probability
- 2019

It is proved that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique, and it is shown that under additional conditions of the approximation, there exists a unique Lipschitz flow.

The non-linear sewing lemma III: Stability and generic properties

- Mathematics
- 2020

Abstract Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme…

Flows driven by rough paths

- Mathematics
- 2012

We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main…

Flows driven by Banach space-valued rough paths

- Mathematics
- 2014

We show in this note how the machinery of \(\mathcal{C}^{1}\)-approximate flows devised in the work Flows driven by rough paths, and applied there to reprove and extend most of the results on Banach…

Semiflow selection and Markov selection theorems

- MathematicsTopological Methods in Nonlinear Analysis
- 2020

The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises…

PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES

- MathematicsForum of Mathematics, Pi
- 2015

We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough…

Perturbed linear rough differential equations

- Mathematics, Computer Science
- 2014

These results provide the key technical point to study the regularity of the dierential of the Ito map in a subsequent article.

Rough flows

- Mathematics, Computer ScienceJournal of the Mathematical Society of Japan
- 2019

This work uses the machinery of approximate flows to build the integration theory of rough drivers and proves well-posedness results for rough differential equations on flows and continuity of the solution flow as a function of the generating rough driver.