Global Existence of Near-Affine Solutions to the Compressible Euler Equations
Sign Up to like & getrecommendations! Published in 2019 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-019-01387-4
Abstract: We establish the global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into a vacuum. Vacuum states can occur with either smooth or singular… read more here.
Keywords: global existence; compressible euler; existence; solutions compressible ... See more keywords
An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and $$L_2$$L2 stability
Sign Up to like & getrecommendations! Published in 2019 at "Numerische Mathematik"
DOI: 10.1007/s00211-019-01027-9
Abstract: The objective of this article is to characterize the entropy and $$L_2$$L2 stability of several representative discontinuous Galerkin (DG) methods for solving the compressible Euler equations. Towards this end, three DG methods are constructed: one… read more here.
Keywords: compressible euler; semi discrete; euler equations; entropy stability ... See more keywords
L1-convergence rates to the Barenblatt solution for the damped compressible Euler equations
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.12.016
Abstract: Abstract In our previous work [17] , it is shown that any L ∞ weak entropy solution of damped compressible Euler equation converges to the Barrenblatt's solution with finite mass in L 1 norm with… read more here.
Keywords: convergence; solution damped; damped compressible; compressible euler ... See more keywords
Radon measure solutions for steady compressible Euler equations of hypersonic-limit conical flows and Newton's sine-squared law
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DOI: 10.1016/j.jde.2019.12.012
Abstract: Abstract We formulate a mathematical problem on hypersonic-limit of three-dimensional steady uniform non-isentropic compressible Euler flows of polytropic gases passing a straight cone with arbitrary cross-section and attacking angle, which is to study Radon measure… read more here.
Keywords: newton sine; compressible euler; measure; radon measure ... See more keywords
Global stability to steady supersonic solutions of the 1-D compressible Euler equations with frictions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124761
Abstract: Abstract In this paper, using wave decomposition and establishing uniform a priori C 1 estimates, we proved global stability of steady supersonic Fanno flows under small perturbations of initial-boundary values in a one-dimensional rectilinear finite… read more here.
Keywords: steady supersonic; compressible euler; stability steady; global stability ... See more keywords
Representing turbulent statistics with partitions of state space. Part 2. The compressible Euler equations
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Fluid Mechanics"
DOI: 10.1017/jfm.2024.657
Abstract: Abstract This is the second part of a two-part paper. We apply the methodology of the first paper (Souza, J. Fluid Mech., vol. 997, 2024, A1) to construct a data-driven finite-volume discretization of the Liouville/Fokker–Planck… read more here.
Keywords: part; state space; compressible euler; state ... See more keywords
Blowup phenomenon for the initial-boundary value problem of the non-isentropic compressible Euler equations
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DOI: 10.1063/1.5031120
Abstract: The blowup phenomenon for the initial-boundary value problem of the non-isentropic compressible Euler equations is investigated. More precisely, we consider a functional F(t) associated with the momentum and weighted by a general test function f… read more here.
Keywords: non isentropic; compressible euler; euler equations; isentropic compressible ... See more keywords
Gradient blowup without shock formation in compressible Euler flow
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DOI: 10.1063/5.0185592
Abstract: The well-known Guderley similarity solution provides a fundamental example of how a spherically converging shock wave can generate amplitude blowup in compressible Euler flow. Recent work has shown that the same phenomenon can occur in… read more here.
Keywords: euler flow; blowup; gradient blowup; compressible euler ... See more keywords
Logarithm Conformation Representation on Compressible Euler Equation and Its Numerical Simulation
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DOI: 10.1080/10618562.2025.2500293
Abstract: Based on logarithm conformation representation, new equations that have the same Riemann invariant as the compressible Euler equations, but are defined in the non-conservation system, were obtained. In the new equations, adaptive mesh refinement, which… read more here.
Keywords: compressible euler; logarithm conformation; conformation representation;
A variational time discretization for compressible Euler equations
Sign Up to like & getrecommendations! Published in 2019 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/7747
Abstract: We introduce a variational time discretization for the multidimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each time step requires the minimization of a functional measuring the acceleration… read more here.
Keywords: time; compressible euler; time discretization; euler equations ... See more keywords