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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.15620 |
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Table of Contents:
- We consider the following parabolic approximation for hyperbolic system of conservation laws in 1-D with non-singular viscosity matrix $B(u)$ and $A(u)$ strictly hyperbolic, \[u^\varepsilon_t+A(u^\varepsilon)u^\varepsilon_x=\varepsilon(B(u^\varepsilon)u^\varepsilon_x)_x.\] We prove global in time uniform $BV$ bound for solution to this parabolic system when $\varepsilon>0$ provided that the initial data is small in $BV$ and the matrix $A(u)$ and $B(u)$ commutate. Moreover, in the case where the system is conservative, we show that the sequence $(u^\varepsilon)_{\varepsilon>0}$ admits a limit $u$, which is the unique global weak solution to the limiting strictly hyperbolic system. We provide a concrete application of this result in the study of the visco-dispersive limit of the Navier-Stokes-Korteweg system.