Breakdown of Smoothness for the Muskat Problem

Ángel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo

doi:10.1007/s00205-013-0616-x

Breakdown of Smoothness for the Muskat Problem

Ángel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo

Mathematics

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

68 Scopus citations

Abstract

In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C⁴.

Original language	English (US)
Pages (from-to)	805-909
Number of pages	105
Journal	Archive for Rational Mechanics and Analysis
Volume	208
Issue number	3
DOIs	https://doi.org/10.1007/s00205-013-0616-x
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-013-0616-x

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title = "Breakdown of Smoothness for the Muskat Problem",

abstract = "In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C4.",

author = "{\'A}ngel Castro and Diego C{\'o}rdoba and Charles Fefferman and Francisco Gancedo",

year = "2013",

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journal = "Archive for Rational Mechanics and Analysis",

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T1 - Breakdown of Smoothness for the Muskat Problem

AU - Castro, Ángel

AU - Córdoba, Diego

AU - Fefferman, Charles

AU - Gancedo, Francisco

PY - 2013/6

Y1 - 2013/6

N2 - In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C4.

AB - In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C4.

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JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

Breakdown of Smoothness for the Muskat Problem

Abstract

All Science Journal Classification (ASJC) codes

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