Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

P. Braz e Silva; F. W. Cruz; M. A. Rojas-Medar; E. G. Santos

doi:10.1016/j.jmaa.2018.12.075

Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

P. Braz e Silva
, F. W. Cruz
, M. A. Rojas-Medar
, E. G. Santos

Department of Mathematics

Universidade Federal de Pernambuco
Universidade Federal da Paraíba

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

12 Scopus citations

Abstract

We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Ω⊊R³, when the initial vacuum is allowed, i.e., the initial density ρ₀ is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms.

Original language	English
Pages (from-to)	567-586
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	473
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.12.075
State	Published - 1 May 2019

Keywords

Asymmetric fluids
Existence
Vacuum
Weak solutions

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10.1016/j.jmaa.2018.12.075

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title = "Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum",

abstract = "We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Ω⊊R3, when the initial vacuum is allowed, i.e., the initial density ρ0 is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms.",

keywords = "Asymmetric fluids, Existence, Vacuum, Weak solutions",

author = "\{Braz e Silva\}, P. and Cruz, \{F. W.\} and Rojas-Medar, \{M. A.\} and Santos, \{E. G.\}",

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doi = "10.1016/j.jmaa.2018.12.075",

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T1 - Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

AU - Braz e Silva, P.

AU - Cruz, F. W.

AU - Rojas-Medar, M. A.

AU - Santos, E. G.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Ω⊊R3, when the initial vacuum is allowed, i.e., the initial density ρ0 is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms.

AB - We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Ω⊊R3, when the initial vacuum is allowed, i.e., the initial density ρ0 is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms.

KW - Asymmetric fluids

KW - Existence

KW - Vacuum

KW - Weak solutions

UR - https://www.scopus.com/pages/publications/85059572955

U2 - 10.1016/j.jmaa.2018.12.075

DO - 10.1016/j.jmaa.2018.12.075

M3 - Article

AN - SCOPUS:85059572955

SN - 0022-247X

VL - 473

SP - 567

EP - 586

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

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Keywords

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