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##### IMI(Institute of Mathematics for Industry)

# Publications

## MI Preprints

2018-5

Title：Long time solutions for the 2D inviscid Boussinesq equations with strong stratification

Author : Ryo Takada

Author : Ryo Takada

Abstract: We consider the initial value problem of the 2D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data with the optimal Sobolev regularity when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the asymptotic profile of the long time solution is given by the corresponding linear dispersive solution.

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2018-5

2018-4

Title：Asymptotic behavior of solutions of the compressible Navier-Stokes equations in a cylinder under the slip boundary condition

Author : Abulizi Aihaiti & Yoshiyuki Kagei

Author : Abulizi Aihaiti & Yoshiyuki Kagei

Abstract: The large time behavior of solutions to the compressible Navier-Stokes equations around the motionless state is considered in a cylinder under the slip boundary condition. It is shown that if the initial data is sufficiently small, the global solution uniquely exists and the large time behavior of the solution is described by a superposition of one-dimensional nonlinear diffusion waves and a diffusive rigid rotation.

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2018-4

2018-3

Title：Global existence of solutions of the compressible viscoelastic ﬂuid around a parallel ﬂow

Author : Yusuke Ishigaki

Author : Yusuke Ishigaki

Abstract: We consider a system of equations for a motion of a compressible viscoelastic ﬂuid in an inﬁnite layer. When the external force has a suitable form, the system has a solution of parallel ﬂow type. It is shown that the solution of the system exists globally in time if the initial data is sufficiently close to the one of the parallel ﬂow, provided that the Reynolds number and the Mach number are suﬃciently small, and that the speed of the propagation of shear wave is suﬃciently large.

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2018-3

2018-2

Title：Effect of Compressibility on Heat-loss and Darrieus-Landau Instability of a Premixed Flame

Author : Keigo Wada & Yasuhide Fukumoto

Author : Keigo Wada & Yasuhide Fukumoto

Abstract: The effect of compressibility on the stability of a premixed flame front is studied theoretically in the form of $M^2$ expansions for small Mach numbers. The method of matched asymptotic expansions are used to derive jump conditions for hydrodynamic variables across a flame front which is separated into the preheat zone and the reaction zone sandwiched in the former. Our analysis captures the heat-loss caused by pressure variation in the heat-conduction equation, a manifestation of the compressibility effect. For calculating the dispersion relation for waves on a planar flame front, we impose translational symmetry to the temperature and the density perturbations in order to obtain the mass-flux condition at the front. We show that, if the Prandtl number and the heat release are sufficiently large, the compressibility effect suppresses the Darrieus-Landau instability.

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2018-2

2018-1

Title：Strongly stratified limit for the 3D inviscid Boussinesq equations

Author : Ryo Takada

Author : Ryo Takada

Abstract: We consider the initial value problem of the 3D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the long time classical solution converges to that of 2D incompressible Euler equations in some space-time Strichartz norms.

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2018-1