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Nonlinear dispersive waves and fluids. AMS special sessions on spectral calculus and quasilinear partial differential equations, and PDE analysis on fluid flows, Atlanta, GA, USA, January 5–7, 2017. (English) Zbl 1414.35005

Contemporary Mathematics 725. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4109-8/pbk; 978-1-4704-5196-7/ebook). x, 275 p. (2019).

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Publisher’s description: This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics.
The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.
The articles of this volume will be reviewed individually.
Indexed articles:
Basharat, Nyla; Hu, Yi; Zheng, Shijun, Blowup rate for mass critical rotational nonlinear Schrödinger equations, 1-12 [Zbl 1423.35348]
Cao, Dat; Mengesha, Tadele; Phan, Tuoc, Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients, 13-33 [Zbl 1428.35116]
Denlinger, Ryan, Virial estimates for hard spheres, 35-52 [Zbl 1423.35291]
Du, Yi; Chen, Geng; Liu, Jianli, The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals, 53-64 [Zbl 1423.35309]
Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana, Instability of solitons – revisited. I: The critical generalized KdV equation, 65-88 [Zbl 1423.35336]
Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana, Instability of solitons – revisited. II: The supercritical Zakharov-Kuznetsov equation, 89-109 [Zbl 1423.35337]
Flores, Cynthia; Oh, Seungly; Smith, Derek, Stabilization of dispersion-generalized Benjamin-Ono, 111-136 [Zbl 1423.35338]
Garrisi, Daniele; Georgiev, Vladimir, Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one, 137-148 [Zbl 1423.35349]
Gustafson, Stephen; Roxanas, Dimitrios, Below-threshold solutions of a focusing energy-critical heat equation in \(\mathbb{R}^4\), 149-162 [Zbl 1423.35133]
Li, Dong; Zhang, Xiaoyi, A regularity upgrade of pressure, 163-185 [Zbl 1423.35300]
Miao, Shuang, On large future-global-in-time solutions to energy-supercritical nonlinear wave equation, 187-214 [Zbl 1428.35229]
Murphy, Jason, The nonlinear Schrödinger equation with an inverse-square potential, 215-225 [Zbl 1423.35352]
Shao, Yuanzhen; Wang, Changyou, The harmonic map heat flow on conic manifolds, 227-250 [Zbl 1448.58022]
Yamazaki, Kazuo, On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian, 251-264 [Zbl 1428.35405]
Zhang, Jian; Zheng, Shijun; Zhu, Shihui, Orbital stability of standing waves for fractional Hartree equation with unbounded potentials, 265-275 [Zbl 1423.35357]

MSC:

35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
35Q35 PDEs in connection with fluid mechanics
35L05 Wave equation
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q53 KdV equations (Korteweg-de Vries equations)
35Q05 Euler-Poisson-Darboux equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
00B25 Proceedings of conferences of miscellaneous specific interest
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