Well-posedness of initial value problem for Euler equations of inviscid compressible adiabatic fluid

Wang Yue-peng
July 2005
Applied Mathematics & Mechanics;Jul2005, Vol. 26 Issue 7, p865
Academic Journal
The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local (exact) solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.


Related Articles

  • Mean value formula for harmonic functions on a circular sector. Moiseev, T. E. // Doklady Mathematics;Jun2010, Vol. 81 Issue 3, p447 

    The article offers information on how to determine the mean value formula for circular mathematical sector's harmonic functions. It presents the solution to delineate the mean value formula's validity for homogeneous boundary conditions. In addition, it cites the statement of the problems along...

  • Types of solutions and approximation of solutions of second order nonlinear boundary value problems. Dobkevich, Mariya; Sadyrbaev, Felix // AIP Conference Proceedings;9/9/2009, Vol. 1168 Issue 1, p260 

    We study non-monotone iterations of solutions of second order boundary value problems in presence of well-ordered lower and upper functions in contrast to monotone iterations. Monotone iterations are known to converge to solutions with the specific feature that the respective equation of...

  • Discrete Quintic Spline for Boundary Value Problem in Plate Deflation Theory. Wong, Patricia J. Y. // AIP Conference Proceedings;2017, Vol. 1863 Issue 1, p1 

    We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to...

  • Existence of Compressible Current-Vortex Sheets: Variable Coefficients Linear Analysis. Trakhinin, Yuri; Liu, T.-P. // Archive for Rational Mechanics & Analysis;Sep2005, Vol. 177 Issue 3, p331 

    We study the initial-boundary value problem resulting from the linearization of the equations of ideal compressible magnetohydrodynamics and the Rankine-Hugoniot relations about an unsteady piecewise smooth solution. This solution is supposed to be a classical solution of the system of...

  • Singular limits in Liouville-type equations. del Pino, Manuel; Kowalczyk, Michal; Musso, Monica // Calculus of Variations & Partial Differential Equations;Sep2005, Vol. 24 Issue 1, p47 

    We consider the boundary value problem $ \Delta u + \varepsilon ^{2} k{\left( x \right)}e^{u} = 0$ in a bounded, smooth domain $\Omega$ in $ \mathbb{R}^{{\text{2}}} $ with homogeneous Dirichlet boundary conditions. Here $$ \varepsilon > 0,k(x) $$ is a non-negative, not identically zero function....

  • Parabolic pseudodifferential equations. Vasil’ev, V.; Kuz’michev, A. // Differential Equations;Mar2006, Vol. 42 Issue 3, p452 

    The article discusses a parabolic version of the theory of the elliptic and parabolic boundary value problems for pseudodifferential equations in the simplest two-dimensional case. All relevant equations, notations and calculations are presented.

  • On boundary value problems for systems of linear generalized ordinary differential equations with singularities. Ashordiya, M. // Differential Equations;Mar2006, Vol. 42 Issue 3, p307 

    The article focuses on the boundary value problems for systems of linear generalized ordinary differential equations with singularities. The existence of a solution of the system of linear generalized ordinary differential equations was analyzed. All relevant equations, solutions and...

  • Existence and Uniqueness of Solution for Fractional Differential Equations with Integral Boundary Conditions. Xiping Liu; Mei Jia; Baofeng Wu // Electronic Journal of Qualitative Theory of Differential Equatio;Dec2009, Special section p1 

    This paper is devoted to the existence and uniqueness results of solutions for fractional differential equations with integral boundary conditions. {CDαx(t) + f(t, x(t), x'(t)) = 0, t ∈ (0, 1), x(0) = ∫10 g0(s, x(s))ds, x(1) = ∫10 g1(s, x(s))ds, x(k)(0) = 0, k = 2, 3, ⋯,...

  • Existence of solution for boundary value problems of differential equations with delay. Xiguang Li // World Academy of Science, Engineering & Technology;Aug2011, Issue 56, p1400 

    In this paper, by using fixed point theorem, upper and lower solution's method and monotone iterative technique, we prove the existence of maximum and minimum solutions of differential equations with delay, which improved and generalize the result of related paper.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics