Geometric flows with rough initial data

By Herbert Koch, T. Lamm. 2009

189 citations recorded by the source corpus.

We show the existence of a global unique and analytic solution for the mean curvature flow, the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. We also show the existence of a global unique and analytic solution to the Ricci-DeTurck flow on euclidean space for bounded initial metrics which are close to the euclidean metric in $L^\infty$ and to the harmonic map flow for initial maps whose image is contained in a small geodesic ball.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9469aaba17a367268938035fad93f74e899cdcb1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Changyou Wang
2. T. Lamm
3. T. Rivière
4. Christoph Scheven
5. Andreas Gastel
6. F. Lin
7. Michael Struwe
8. Valentino Magnani

In Astronomy and Astrophysics

1. Changyou Wang

In Geometry and Topology

1. Changyou Wang
2. T. Lamm
3. T. Rivière
4. Andreas Gastel
5. Christoph Scheven
6. Michael Struwe
7. Valentino Magnani

Citations in the corpus

• Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data (2010, methodology): “Partially motivated by [10] and [11], we address the well-posedness for both the heat flow of harmonic maps and the hydrodynamic flow of nematic liquid crystals in this paper.”