A note on stability shifting for the Muskat problem

Diego Córdoba; Javier Gómez-Serrano; Andrej Zlato

doi:10.1098/rsta.2014.0278

A note on stability shifting for the Muskat problem

Diego Córdoba
, Javier Gómez-Serrano
, Andrej Zlato

Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L^∞ norm of the derivative of the initial condition that develop a turning singularity.

Original language	English (US)
Article number	20140278
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	373
Issue number	2050
DOIs	https://doi.org/10.1098/rsta.2014.0278
State	Published - Sep 13 2015

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering
General Physics and Astronomy

Keywords

Incompressible fluid
Interface
Muskat problem
Porous media
Rayleigh-Taylor

Access to Document

10.1098/rsta.2014.0278

Cite this

@article{be3d8db9ad12431fa67fb510f6490ac7,

title = "A note on stability shifting for the Muskat problem",

abstract = "In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L∞ norm of the derivative of the initial condition that develop a turning singularity.",

keywords = "Incompressible fluid, Interface, Muskat problem, Porous media, Rayleigh-Taylor",

author = "Diego C{\'o}rdoba and Javier G{\'o}mez-Serrano and Andrej Zlato",

year = "2015",

month = sep,

day = "13",

doi = "10.1098/rsta.2014.0278",

language = "English (US)",

volume = "373",

journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "1364-503X",

publisher = "Royal Society of London",

number = "2050",

}

TY - JOUR

T1 - A note on stability shifting for the Muskat problem

AU - Córdoba, Diego

AU - Gómez-Serrano, Javier

AU - Zlato, Andrej

PY - 2015/9/13

Y1 - 2015/9/13

N2 - In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L∞ norm of the derivative of the initial condition that develop a turning singularity.

AB - In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L∞ norm of the derivative of the initial condition that develop a turning singularity.

KW - Incompressible fluid

KW - Interface

KW - Muskat problem

KW - Porous media

KW - Rayleigh-Taylor

UR - https://www.scopus.com/pages/publications/84939160525

UR - https://www.scopus.com/pages/publications/84939160525#tab=citedBy

U2 - 10.1098/rsta.2014.0278

DO - 10.1098/rsta.2014.0278

M3 - Article

C2 - 26261369

AN - SCOPUS:84939160525

SN - 1364-503X

VL - 373

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2050

M1 - 20140278

ER -

A note on stability shifting for the Muskat problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this