Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

Albert Clop; Heikki Jylhä; Joan Orobitg; Juan Eugenio Mateu Bennassar

doi:10.1016/j.jfa.2018.10.001

Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

Albert Clop, Heikki Jylhä, Joan Orobitg, Juan Eugenio Mateu Bennassar

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Abstract

We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H-1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function. (C) 2018 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	45-77
Number of pages	33
Journal	Journal of Functional Analysis
Volume	276
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2018.10.001
Publication status	Published - 1 Jan 2019

Keywords

Continuity equation
EULER EQUATIONS
Hardy space
Mass transport
ORDINARY DIFFERENTIAL-EQUATIONS
TRANSPORT-EQUATION
UNIQUENESS

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10.1016/j.jfa.2018.10.001

https://ddd.uab.cat/record/288144

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title = "Well-posedness for the continuity equation for vector fields with suitable modulus of continuity",

abstract = "We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H-1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function. (C) 2018 Elsevier Inc. All rights reserved.",

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T1 - Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

AU - Clop, Albert

AU - Jylhä, Heikki

AU - Orobitg, Joan

AU - Mateu Bennassar, Juan Eugenio

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H-1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function. (C) 2018 Elsevier Inc. All rights reserved.

AB - We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H-1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function. (C) 2018 Elsevier Inc. All rights reserved.

KW - Continuity equation

KW - EULER EQUATIONS

KW - Hardy space

KW - Mass transport

KW - ORDINARY DIFFERENTIAL-EQUATIONS

KW - TRANSPORT-EQUATION

KW - UNIQUENESS

UR - http://www.mendeley.com/research/wellposedness-continuity-equation-vector-fields-suitable-modulus-continuity

U2 - 10.1016/j.jfa.2018.10.001

DO - 10.1016/j.jfa.2018.10.001

M3 - Article

SN - 0022-1236

VL - 276

SP - 45

EP - 77

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

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Keywords

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