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  1. No Access

    Chapter

    On the Work of Jean Bourgain in Nonlinear Dispersive Equations

    In this brief note, we survey a sample of the deep and influential contributions of Jean Bourgain to the field of nonlinear dispersive equations. Bourgain also made many fundamental contributions to other area...

    Carlos E. Kenig in Analysis at Large (2022)

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    Article

    Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line

    In this paper we show that the flow map of the Benjamin-Ono equation on the line is weakly continuous in L 2(ℝ), using “local smoothing” estimates. L 2(ℝ) is believ...

    Shangbin Cui, Carlos E. Kenig in Journal of Fourier Analysis and Applications (2010)

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    Chapter

    Recent Progress on the Global Well-Posedness of the KPI Equation

    In this chapter I survey the well-posedness theory for the Kadomtsev–Petviashvili (KPI) equation, culminating with the recent proof (joint with A. Ionescu and D. Tataru) of the global well-posedness of the KPI...

    Carlos E. Kenig in Recent Developments in Real and Harmonic Analysis (2010)

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    Article

    A Liouville theorem for the viscous Burgers’s equation

    Carlos E. Kenig, Frank Merle in Journal d'Analyse Mathématique (2002)

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    Article

    The absolute continuity of elliptic measure revisited

    Carlos E. Kenig, Jill Pipher in Journal of Fourier Analysis and Applications (1998)

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    Article

    Local well-posedness for higher order nonlinear dispersive systems

    We study nonlinear dispersive systems of the form $$\partial _t u_k + \partial _x^{(2j + 1)} uk + P_k (u_l , \ldots u_n , \ldots ,\pa...

    Carlos E. Kenig, Gigliola Staffilani in Journal of Fourier Analysis and Applications (1997)

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    Article

    Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure

    Carlos E. Kenig in Journal of Fourier Analysis and Applications (1997)