منابع مشابه
Refraction of dispersive shock waves
We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The dispersive shock wave (DSW) refraction due to its head-on collision with the centred rarefaction wave (RW) is considered in the frameworks of the one-dimensional defocusing nonlinear Schr...
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Dispersive hydrodynamics is the domain of applied mathematics and physics concerned with fluid motion in which internal friction, e.g., viscosity, is negligible relative to wave dispersion. In conservative media such as superfluids, optical materials, and water waves, nonlinearity has the tendency to engender wavebreaking that is mitigated by dispersion. The mathematical framework for such medi...
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In this short expository note, we will discuss three subjects: dispersive estimates, Strichartz estimates and smoothing effects which are of great importance in the study of dispersive equations. We will focus on the Euclidean setting and try to derive the interplay among above three objects. We will mainly focus on linear problems in various contexts. Some nonlinear application will also be me...
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The Euler–Korteweg system consists of a quasi-linear, dispersive perturbation of the Euler equations. The Cauchy problem has been studied in any dimension d ≥ 1 by Benzoni, Danchin, and Descombes, who obtained local well-posedness results when the velocity is in Hs for s > d/2 + 1. They noticed that one may expect to find some smoothing effect due to the dispersive effects, but there was no pro...
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ژورنال
عنوان ژورنال: Journées équations aux dérivées partielles
سال: 1993
ISSN: 0752-0360
DOI: 10.5802/jedp.451