Journal ArticleDOI
Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
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This article is published in Duke Mathematical Journal.The article was published on 1993-05-01. It has received 102 citations till now. The article focuses on the topics: Asymptotic analysis & Singular perturbation.read more
Citations
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Regularity and integrability of 3D Euler and Navier–Stokes equations for rotating fluids
TL;DR: In this article, the authors consider 3D Euler and Navier-Stokes equations describing dynamics of uniformly rotating fluids and show that solutions of these equations can be decomposed as U(t, x1, x2, x3) + r, where r is a solution of the 2D NN system with vertically averaged initial data (axis of rotation is taken along the vertical e3).
Book
Hyperbolic Partial Differential Equations and Geometric Optics
TL;DR: In this article, the authors introduce graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed.
Journal ArticleDOI
Applications of Schochet's methods to parabolic equations
TL;DR: In this article, a diffusion term has been added, with the minimal assumption on the Sobolev regularity of the initial data (Hd2−1 in the d-dimensional torus).
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Diffractive nonlinear geometric optics with rectification
TL;DR: In this paper, the authors propose a method to solve the problem of "uniformity" and "uncertainty" in the context of health care, and propose a solution.
References
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Journal ArticleDOI
Resonantly interacting, weakly nonlinear hyperbolic waves.II. Several space variables
John K. Hunter,John K. Hunter,John K. Hunter,Andrew J. Majda,Andrew J. Majda,Andrew J. Majda,R Rosales,R Rosales,R Rosales +8 more
TL;DR: In this article, the authors present a systematic asymptotic theory for resonantly interacting weakly nonlinear hyperbolic waves in a single space variable, which includes as a special case the theory of nonresonant interacting waves for general Hyperbolic systems developed recently by J. Hunter and J. B. Keller.
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Weakly nonlinear high frequency waves
John K. Hunter,Joseph B. Keller +1 more
TL;DR: In this paper, the authors derived a method for finding small amplitude high frequency solutions to hyperbolic systems of quasilinear partial differential equations, where each high frequency wave displays nonlinear distortion of the wave profile and shocks may form.
Journal ArticleDOI
Resonant One Dimensional Nonlinear Geometric Optics
TL;DR: In this paper, the existence and resonant interaction of oscillatory wave trains in one space dimension was studied, and a rigorous proof of the validity of the corresponding expansions of weakly nonlinear optics was given.