On the existence of global smooth solutions for a model equation for fluid flow in a pipe

Mitchell Luskin

doi:10.1016/0022-247X(81)90192-X

On the existence of global smooth solutions for a model equation for fluid flow in a pipe

Mitchell Luskin

School of Mathematics

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

15 Scopus citations

Abstract

We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small.

Original language	English (US)
Pages (from-to)	614-630
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	84
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(81)90192-X
State	Published - Dec 1981

Bibliographical note

Funding Information:
* Supported by AFOSR under Contract F49620-79-C-0149 at the &ole Polytechnique Fed&ale, Lausanne. Switzerland.

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10.1016/0022-247X(81)90192-X

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title = "On the existence of global smooth solutions for a model equation for fluid flow in a pipe",

abstract = "We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small.",

author = "Mitchell Luskin",

note = "Funding Information: * Supported by AFOSR under Contract F49620-79-C-0149 at the &ole Polytechnique Fed&ale, Lausanne. Switzerland.",

year = "1981",

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PY - 1981/12

Y1 - 1981/12

N2 - We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small.

AB - We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small.

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On the existence of global smooth solutions for a model equation for fluid flow in a pipe

Abstract

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