Singularity formation for one dimensional full Euler equations
نویسندگان
چکیده
منابع مشابه
Singularity formation for compressible Euler equations
In this paper, for the p-system and full compressible Euler equations in one space dimension, we provide an equivalent and a sharp condition on initial data, respectively, under which the classical solution must break down in finite time. Moreover, we provide time-dependent lower bounds on density for arbitrary classical solutions for these two equations. Our results have no restriction on the ...
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Michael P. Brenner,1 Sahand Hormoz,2,3 and Alain Pumir4 1School of Engineering and Applied Sciences and Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA 3Division of Biology and Biological Engineering, California Insti...
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The analytic properties of adjoint solutions are examined for the quasi-onedimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is required at the shock. A Green’s function approach is used to derive the analytic adjoint solutions cor...
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Article history: Received 6 March 2008 Received in revised form 8 September 2008 Accepted 24 September 2008 Available online 10 October 2008
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We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize P. Lax’s singularity (shock) formation results in [9] for hyperbolic systems with two variables to the 3× 3 compressible Euler eq...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2016
ISSN: 0022-0396
DOI: 10.1016/j.jde.2016.09.015