Advances in Differential Equations

On the system of conservation laws and its perturbation in the Besov spaces

Dongho Chae

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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.

Article information

Source
Adv. Differential Equations Volume 10, Number 9 (2005), 983-1006.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867814

Mathematical Reviews number (MathSciNet)
MR2161756

Zentralblatt MATH identifier
1103.35071

Subjects
Primary: 35L65: Conservation laws
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Citation

Chae, Dongho. On the system of conservation laws and its perturbation in the Besov spaces. Adv. Differential Equations 10 (2005), no. 9, 983--1006. https://projecteuclid.org/euclid.ade/1355867814.


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