TITLE

The expansion of a wedge of gas into vacuum with small angle in two-dimensional isothermal flow

AUTHOR(S)
Ge, Ju; Sheng, Wancheng
PUB. DATE
May 2016
SOURCE
Chinese Annals of Mathematics;May2016, Vol. 37 Issue 3, p395
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case $$0 < \theta \leqslant \bar \theta = \arctan \tfrac{1} {{\sqrt {2 + \sqrt 5 } }}$$, where θ is the half angle of the wedge. Furthermore, they get the uniform C estimates of the solution to the expansion problem.
ACCESSION #
114818664

 

Related Articles

  • A Fast Augmented Lagrangian Method for Euler's Elastica Models. Yuping Duan; Yu Wang; Jooyoung Hahn // Numerical Mathematics: Theory, Methods & Applications;Feb2013, Vol. 6 Issue 1, p47 

    In this paper, a fast algorithm for Euler's elastica functional is proposed, in which the Euler's elastica functional is reformulated as a constrained minimization prob-lem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved...

  • The 3D Incompressible Euler Equations with a Passive Scalar: A Road to Blow-Up? Gibbon, John D.; Titi, Edriss S. // Journal of Nonlinear Science;Dec2013, Vol. 23 Issue 6, p993 

    The three-dimensional incompressible Euler equations with a passive scalar θ are considered in a smooth domain $\varOmega\subset \mathbb{R}^{3}$ with no-normal-flow boundary conditions $\boldsymbol{u}\cdot\hat{\boldsymbol{n}}|_{\partial\varOmega} = 0$ . It is shown that smooth solutions blow...

  • Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes. Gan Yin; Kyungwoo Song // Abstract & Applied Analysis;2013, p1 

    Vanishing pressure limits of Riemann solutions to relativistic Euler system for Chaplygin gas are identified and analyzed in detail. Unlike the polytropic or barotropic gas case, as the parameter decreases to a critical value, the two-shock solution converges firstly to a delta shock wave...

  • Free Vibration Analysis of an Euler Beam of Variable Width on the Winkler Foundation Using Homotopy Perturbation Method. Mutman, Utkan // Mathematical Problems in Engineering;2013, p1 

    Homotopy Perturbation Method (HPM) is employed to investigate the vibration of an Euler beamresting on an elastic foundation. The beam is assumed to have variable stiffness along its length. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear...

  • THE TWO DIMENSIONAL GAS EXPANSION PROBLEM OF THE EULER EQUATIONS FOR THE GENERALIZED CHAPLYGIN GAS. JU GE; WANCHENG SHENG; Zhen Lei // Communications on Pure & Applied Analysis;Nov2014, Vol. 13 Issue 6, p2733 

    The collapse of a wedge-shaped dam containing fluid initially with a uniform velocity can be described as an expansion problem of gas into vacuum. It is an important class of binary interaction of rarefaction waves in the two dimensional Riemann problems for the compressible Euler equations. In...

  • A Fast Augmented Lagrangian Method for Euler's Elastica Models. Yuping Duan; Yu Wang; Jooyoung Hahn // Numerical Mathematics: Theory, Methods & Applications;Feb2013, Vol. 6 Issue 1, p47 

    In this paper, a fast algorithm for Euler's elastica functional is proposed, in which the Euler's elastica functional is reformulated as a constrained minimization prob-lem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved...

  • Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle. Li, Jun; Xin, Zhouping; Yin, Huicheng // Archive for Rational Mechanics & Analysis;Feb2013, Vol. 207 Issue 2, p533 

    In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, ): given the appropriately large exit pressure p( x), if the...

  • A Regularity Result for the Incompressible Euler Equation with a Free Interface. Kukavica, Igor; Tuffaha, Amjad // Applied Mathematics & Optimization;Jun2014, Vol. 69 Issue 3, p337 

    We address the local existence of solutions of the 2D and 3D water wave problems. For the space dimension three, we consider the irrotational datum u and prove that the local in time existence holds for initial velocities belonging to H, where δ>0 is arbitrary. For the space dimension two,...

  • On the Flux Problem in the Theory of Steady Navier-Stokes Equations with Nonhomogeneous Boundary Conditions. Korobkov, Mikhail; Pileckas, Konstantin; Russo, Remigio // Archive for Rational Mechanics & Analysis;Jan2013, Vol. 207 Issue 1, p185 

    We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional, bounded, multiply connected domain $${\Omega = \Omega_1 \backslash \overline{\Omega}_2, \overline\Omega_2\subset \Omega_1}$$ . We prove that...

  • A vortex of eigenvalues. Crowdy, D. G. // Europhysics News;2014, Vol. 45 Issue 4, p11 

    An abstract of the article "Vortex patch equilibria of the Euler equation and random normal matrices," by D. G. Crowdy is presented.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

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

Try another library?
Sign out of this library

Other Topics