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Global smooth flows for compressible Navier–Stokes–Maxwell equations
- Source :
- Zeitschrift für angewandte Mathematik und Physik. 67
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- Umeda et al. (Jpn J Appl Math 1:435–457, 1984) considered a rather general class of symmetric hyperbolic–parabolic systems: $$A^{0}z_{t}+\sum_{j=1}^{n}A^{j}z_{x_{j}}+Lz=\sum_{j,k=1}^{n}B^{jk}z_{x_{j}x_{k}}$$ and showed optimal decay rates with certain dissipative assumptions. In their results, the dissipation matrices $${L}$$ and $${B^{jk}(j,k=1,\ldots,n)}$$ are both assumed to be real symmetric. So far there are no general results in case that $${L}$$ and $${B^{jk}}$$ are not necessarily symmetric, which is left open now. In this paper, we investigate compressible Navier–Stokes–Maxwell (N–S–M) equations arising in plasmas physics, which is a concrete example of hyperbolic–parabolic composite systems with non-symmetric dissipation. It is observed that the Cauchy problem for N–S–M equations admits the dissipative mechanism of regularity-loss type. Consequently, extra higher regularity is usually needed to obtain the optimal decay rate of $${L^{1}({\mathbb{R}}^3)}$$ - $${L^2({\mathbb{R}}^3)}$$ type, in comparison with that for the global-in-time existence of smooth solutions. In this paper, we obtain the minimal decay regularity of global smooth solutions to N–S–M equations, with aid of $${L^p({\mathbb{R}}^n)}$$ - $${L^{q}({\mathbb{R}}^n)}$$ - $${L^{r}({\mathbb{R}}^n)}$$ estimates. It is worth noting that the relation between decay derivative orders and the regularity index of initial data is firstly found in the optimal decay estimates.
- Subjects :
- Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
General Physics and Astronomy
Type (model theory)
01 natural sciences
010101 applied mathematics
Combinatorics
symbols.namesake
Maxwell's equations
Compressibility
symbols
Dissipative system
Initial value problem
Navier stokes
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14209039 and 00442275
- Volume :
- 67
- Database :
- OpenAIRE
- Journal :
- Zeitschrift für angewandte Mathematik und Physik
- Accession number :
- edsair.doi...........cbe345ff735b14a421a91fa6ad720757