Global regularity for gravity unstable Muskat bubbles / Francisco Gancedo, Eduardo García-Juárez, Neel Patel, Robert M. Strain.

Format:

Book

Author/Creator:

Gancedo, Francisco, author.

Garcia-Juárez, Eduardo, author.

Patel, Neel (Neel J.), author.

Strain, Robert M., author.

Series:

Memoirs of the American Mathematical Society ; no. 1455.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1455.

Language:

English

Subjects (All):

Fluid dynamics.

Differential equations, Partial.

Physical Description:

v, 87 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2023]

Summary:

"In this paper, we study the dynamics of fluids in porous media governed by Darcy's law: the Muskat problem. We consider the setting of two immiscible fluids of different densities and viscosities under the influence of gravity in which one fluid is completely surrounded by the other. This setting is gravity unstable because along a portion of the interface, the denser fluid must be above the other. Surprisingly, even without capillarity, the circle-shaped bubble is a steady state solution moving with vertical constant velocity determined by the density jump between the fluids. Taking advantage of our discovery of this steady state, we are able to prove global in time existence and uniqueness of dynamic bubbles of nearly circular shapes under the influence of surface tension. We prove this global existence result for low regularity initial data. Moreover, we prove that these solutions are instantly analytic and decay exponentially fast in time to the circle." -- Provided by publisher

Contents:

Introduction

Contour dynamics formulation

Notation and main results

Implicit function theorem

Fourier multiplier estimates

A priori estimates on the voracity strength

Global existence and instant analyticity

Uniqueness

Notes:

"December 2023, volume 292, number 1455 (fifth of 6 numbers)."

Includes bibliographical references (pages 85-87).

ISBN:

147046764X

9781470467647

OCLC:

1416951592