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2005 On the system of conservation laws and its perturbation in the Besov spaces
Dongho Chae
Adv. Differential Equations 10(9): 983-1006 (2005).

Abstract

We prove that a system of conservation laws on $ \mathbb R^N$ is locally well posed in the `critical' Besov space $B^{\frac{N}{2} +1}_{2,1}$. The time of local existence depends only on the size of the inhomogeneous part of the initial data. We also obtain a blow-up criterion of the local solution. For the conservation system with a dissipation term added we prove global existence of solutions under the assumption of smallness of the homogeneous part of the arbitrary-sized $B^{\frac{N}{2} -1}_{2,1}$ norm of the initial data. For the proof of these results we essentially use the Littlewood-Paley decomposition of functions to derive the energy type of estimate.

Citation

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Dongho Chae. "On the system of conservation laws and its perturbation in the Besov spaces." Adv. Differential Equations 10 (9) 983 - 1006, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1103.35071
MathSciNet: MR2161756

Subjects:
Primary: 35L65
Secondary: 46E35

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 9 • 2005
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