**Contemporary Mathematics**

Volume: 725;
2019;
275 pp;
Softcover

MSC: Primary 35; 37; 47; 58; 76; 93;

**Print ISBN: 978-1-4704-4109-8
Product Code: CONM/725**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

**Electronic ISBN: 978-1-4704-5196-7
Product Code: CONM/725.E**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

# Nonlinear Dispersive Waves and Fluids

Share this page *Edited by *
*Shijun Zheng; Marius Beceanu; Jerry Bona; Geng Chen; Tuoc Van Phan; Avy Soffer*

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.

#### Readership

Graduate students and research mathematicians interested in analysis, PDEs, and fluid dynamics.

# Table of Contents

## Nonlinear Dispersive Waves and Fluids

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Combined List of Speakers ix10
- Blowup rate for mass critical rotational nonlinear Schrödinger equations 112
- Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients 1324
- Virial estimates for hard spheres 3546
- The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals 5364
- Instability of solitons–revisited, I: The critical generalized KdV equation 6576
- Instability of solitons–revisited, II: The supercritical Zakharov-Kuznetsov equation 89100
- Stabilization of dispersion-generalized Benjamin-Ono 111122
- Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one 137148
- Below-threshold solutions of a focusing energy-critical heat equation in ℝ⁴ 149160
- A regularity upgrade of pressure 163174
- On large future-global-in-time solutions to energy-supercritical nonlinear wave equation 187198
- The nonlinear Schrödinger equation with an inverse-square potential 215226
- The harmonic map heat flow on conic manifolds 227238
- 1. Introduction 227238
- 2. Function spaces on conic manifolds 230241
- 3. The Laplace-Beltrami operator 235246
- 4. Short time existence of the harmonic map heat flow on conic manifolds 240251
- 5. Global existence of the harmonic map heat flow into manifolds with nonpositive sectional curvature 246257
- 6. Acknowledgements 249260
- References 249260

- On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian 251262
- Orbital stability of standing waves for fractional Hartree equation with unbounded potentials 265276
- Back Cover Back Cover1290