Takeyuki Nagasawa

On the outer pressure problem of the one-dimensional polytropic ideal gas

In this paper the existence of the global solution of the outer pressure problem of the one-dimensional polytropic ideal gas is proved (Theorem 1). We shall also investigate, under some suitable assumptions, the convergence of the solution to a stationary state (Theorem 2), and the rate of its convergene (Theorem 3).

Global asymptotics of the outer pressure problem with free boundary

Global asymptotics on the outer pressure problem of free type is discussed. The solution of the problem exists globally (Theorem 1), and some global asymptotics are investigated (Theorem 2). Under some additional assumptions, the solution converges to a stationary state (Theorem 3) with exponential rate (Theorem 4).

On the One-dimensional Free Boundary Problem for the Heat-conductive Compressible Viscous Gas

Publisher Summary This chapter discusses the one-dimensional free boundary problem for the heat-conductive compressible viscous gas. It considers that the one-dimensional motion of the fluid, which satisfies the equations of state of the polytropic ideal gas, with the prescribed stress on the boundary and with adiabatic ends. By use of the Eulerian coordinate system, the motion of the gas is described as the free boundary problem by the following three equations corresponding to the conservation laws of the mass, moment and energy. It mainly discusses the large-time behavior of solution. This chapter aims to show that the global solution converges to the state when P (t) does to the positive constant P for arbitrary initial data.

A New Energy Inequality and Partial Regularity for weak Solutions of Navier—Stokes Equations

Abstract. In this paper we prove a new energy inequality for weak solutions of Leray—Hopf type for the three-dimensional Navier—Stokes equations. It implies a result of partial regularity.

Weak Solutions of a Semilinear Hyperbolic System on a Nondecreasing Domain

The initial-boundary value problem in non-cylindrical domain for a semilinear hyperbolic system is investigated. A weak solution is constructed by the method of semidiscretization in time variable combining with variational calculus, when the time sections of domain has non-decreasing property.