Global existence for viscous systems of conservation laws in Lp framework
Abstract
In this paper, which originates from Chapter 4 of the author's PhD thesis [1, Chap. 4], we investigate the global well-posedness of a class of partially diffusive hyperbolic systems in critical homogeneous Besov spaces. Our main objective is to extend the analysis developed in our previous work [2] to a functional framework in which the high-frequency com- ponents of the solution are controlled in Lp-based spaces with p > 2. This broader framework allows us to establish global existence under weaker smallness assumptions on the initial data and provides more precise information on the qualitative behavior of the resulting solutions. In particular, our analysis yields refined regularity. As an application, our global existence theorem applies to the multidimensional compressible Fourier-Navier-Stokes system
Related
- Asymptotic Stability and Lp Time-Decay Rates of Rarefaction Waves for Systems of Viscous Conservation Laws
- Global boundary stabilization of 1d systems of scalar conservation laws
- Global existence and convergence of a density heat flow for strictly subcritical Liouville systems
- Global Existence and Scattering of a Class of Two-Dimensional Euler--Poisson--Korteweg Systems
- Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms
BibTeX
@misc{adogbo2026global,
title = {{Global existence for viscous systems of conservation laws in $L^p$ framework}},
author = {Jean-Paul Adogbo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03011},
eprint = {2610.03011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global existence for viscous systems of conservation laws in L^p framework
AU - Jean-Paul Adogbo
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03011
UR - https://arxiv.org/abs/2610.03011
AB - In this paper, which originates from Chapter 4 of the author's PhD thesis [1, Chap. 4], we investigate the global well-posedness of a class of partially diffusive hyperbolic systems in critical homogeneous Besov spaces. Our main objective is to extend the analysis developed in our previous work [2] to a functional framework in which the high-frequency com- ponents of the solution are controlled in L^p-based spaces with p > 2. This broader framework allows us to establish global existence under weaker smallness assumptions on the initial data and provides more precise information on the qualitative behavior of the resulting solutions. In particular, our analysis yields refined regularity. As an application, our global existence theorem applies to the multidimensional compressible Fourier-Navier-Stokes system
ER -