Akitaka Matsumura
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Akitaka Matsumura has a total of 10 co-authors. Here are the top co-authors by number of shared publications:
- Hai-Liang Li
School of Mathematical Sciences, Capital Normal University, Beijing, China
3 shared publications - Guojing Zhang
Department of Mathematics, Harbin Institute of Technology, Harbin, People’s Republic of China
2 shared publications - Itsuko Hashimoto
Kanazawa University, Kanazawa, Japan
2 shared publications Feimin Huang
Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Japan
1 shared publication- Feimin Huang
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
1 shared publication - Itsuko Hashimoto
Kanazawa University, Osaka City University, Oksaka, Japan
1 shared publication
Latest Publications
- Open Access
Existence of radially symmetric stationary solutions for viscous and Heat-conductive ideal Gas
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are prescribed. The unique existence of the stationary solution is shown for both inflow and outflow problems in a suitably small neighborhood of the far-field state. Estimates of the algebraic decay rate toward the far field state are also obtained.
Open AccessExistence of radially symmetric stationary solutions for viscous and Heat-conductive ideal Gas
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are prescribed. The unique existence of the stationary solution is shown for both inflow and outflow problems in a suitably small neighborhood of the far-field state. Estimates of the algebraic decay rate toward the far field state are also obtained.
- 24 August 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (9) , 1-20
Inviscid Limit Problem of Radially Symmetric Stationary Solutions for Compressible Navier–Stokes Equation
- 24 August 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (9) , 1-20
Inviscid Limit Problem of Radially Symmetric Stationary Solutions for Compressible Navier–Stokes Equation
- 1 January 2021
- Published by International Press of Boston in Methods and Applications of Analysis
- Vol. 28 (3) , 299-312
Existence of radially symmetric stationary solutions for the compressible Navier–Stokes equation
- 1 January 2021
- Published by International Press of Boston in Methods and Applications of Analysis
- Vol. 28 (3) , 299-312
Existence of radially symmetric stationary solutions for the compressible Navier–Stokes equation
- Open Access
Global asymptotics toward rarefaction waves for solutions of the scalar conservation law with nonlinear viscosity
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.
Open AccessGlobal asymptotics toward rarefaction waves for solutions of the scalar conservation law with nonlinear viscosity
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.
- 6 April 2018
- Published by Springer Nature
- p. 2495-2548
Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
- 6 April 2018
- Published by Springer Nature
- p. 2495-2548
Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
- 29 September 2016
- Published by Springer Nature
- p. 1-55
Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
- 29 September 2016
- Published by Springer Nature
- p. 1-55
Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
- 17 November 2009
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 197 (1) , 89-116
Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System
- 17 November 2009
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 197 (1) , 89-116
Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System
- Open Access
- 21 July 2009
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 196 (2) , 681-713
Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in ${\mathbb {R}^3}$- 21 July 2009
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 196 (2) , 681-713
Open AccessOptimal Decay Rate of the Compressible Navier–Stokes–Poisson System in ${\mathbb {R}^3}$ - Open Access
Optimal decay rate of the compressible Navier-Stokes-Poisson system in R^3
The compressible Navier-Stokes-Poisson (NSP) system is considered in $R^3$ in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ respectively as the compressible Navier-Stokes system, but the momentum of the NSP system decays at the $L^2$-rate $(1+t)^{-\frac14}$ or $L^\infty$-rate $(1+t)^{-1}$ respectively, which is slower than the $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ for the compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the compressible NSP system.Open AccessOptimal decay rate of the compressible Navier-Stokes-Poisson system in R^3
The compressible Navier-Stokes-Poisson (NSP) system is considered in $R^3$ in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ respectively as the compressible Navier-Stokes system, but the momentum of the NSP system decays at the $L^2$-rate $(1+t)^{-\frac14}$ or $L^\infty$-rate $(1+t)^{-1}$ respectively, which is slower than the $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ for the compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the compressible NSP system. - 24 April 2008
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 189 (1) , 1-44
Behaviour of the Fokker–Planck–Boltzmann equation near a Maxwellian
- 24 April 2008
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 189 (1) , 1-44
Behaviour of the Fokker–Planck–Boltzmann equation near a Maxwellian