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.
N. Basharat, Y. Hu, and S. Zheng, Blowup rate for mass critical
rotational nonlinear Schrodinger equations
D. Cao, T. Mengesha, and T. Phan, Gradient estimates for weak solutions of
linear elliptic systems with singular-degenerate coefficients
R. Denlinger, Virial estimates for hard spheres
Y. Du, G. Chen, and J. Liu, The almost global existence to classical solution
for a 3-D wave equation of nematic liquid-crystals
L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited,
I: The critical generalized KdV equation
L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited,
II: The supercritical Zakharov-Kuznetsov equation
C. Flores, S. Oh, and D. Smith, Stabilization of dispersion-generalized
Benjamin-Ono
D. Garrisi and V. Georgiev, Uniqueness of standing-waves for a non-linear
Schrodinger equation with three pure-power combinations in dimension one
S. Gustafson and D. Roxanas, Below-threshold solutions of a focusing
energy-critical heat equation in $\mathbb{R}^4$
D. Li and X. Zhang, A regularity upgrade of pressure
S. Miao, On large future-global-in-time solutions to energy-supercritical
nonlinear wave equation
J. Murphy, The nonlinear Schrodinger equation with an inverse-square
potential
Y. Shao and C. Wang, The harmonic map heat flow on conic manifolds
K. Yamazaki, On the global regularity issue of the two-dimensional
magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian
J. Zhang, S. Zheng, and S. Zhu, Orbital stability of standing waves for
fractional Hartree equation with unbounded potentials.
Shijun Zheng, Georgia Southern University, Statesboro, GA.
Marius Beceanu, University at Albany, NY.
Jerry Bona, University of Illinois at Chicago, IL.
Geng Chen, University of Kansas, Lawrence, KS.
Tuoc Van Phan, University of Tennessee, Knoxville, TN.
Avy Soffer, Rutgers University, Piscataway, NJ.
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