### Abstract

Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L^{1}(R^{n})-L^{2}(R^{n}). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of L^{p}(R^{n})-L^{q}(R^{n})-L^{r}(R^{n}) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler-Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the L^{p}-version.

Original language | English |
---|---|

Pages (from-to) | 965-981 |

Number of pages | 17 |

Journal | Journal des Mathematiques Pures et Appliquees |

Volume | 104 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Euler-Maxwell equations
- L<sup>p</sup>-L<sup>q</sup>-L<sup>r</sup> estimates
- Minimal decay regularity
- Regularity-loss

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**L ^{p}-L^{q}-L^{r} estimates and minimal decay regularity for compressible Euler-Maxwell equations.** / Xu, Jiang; Mori, Naofumi; Kawashima, Shuichi.

Research output: Contribution to journal › Article

^{p}-L

^{q}-L

^{r}estimates and minimal decay regularity for compressible Euler-Maxwell equations',

*Journal des Mathematiques Pures et Appliquees*, vol. 104, no. 5, pp. 965-981. https://doi.org/10.1016/j.matpur.2015.07.001

}

TY - JOUR

T1 - Lp-Lq-Lr estimates and minimal decay regularity for compressible Euler-Maxwell equations

AU - Xu, Jiang

AU - Mori, Naofumi

AU - Kawashima, Shuichi

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L1(Rn)-L2(Rn). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of Lp(Rn)-Lq(Rn)-Lr(Rn) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler-Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the Lp-version.

AB - Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L1(Rn)-L2(Rn). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of Lp(Rn)-Lq(Rn)-Lr(Rn) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler-Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the Lp-version.

KW - Euler-Maxwell equations

KW - L<sup>p</sup>-L<sup>q</sup>-L<sup>r</sup> estimates

KW - Minimal decay regularity

KW - Regularity-loss

UR - http://www.scopus.com/inward/record.url?scp=84941751922&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941751922&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2015.07.001

DO - 10.1016/j.matpur.2015.07.001

M3 - Article

AN - SCOPUS:84941751922

VL - 104

SP - 965

EP - 981

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

IS - 5

ER -