Koike S., Kozono H., Ogawa T., Sakaguchi S. (Eds.) Nonlinear Partial Differential Equations for Future Applications: Sendai, Japan, July 10-28 and October 2-6, 2017

Springer, 2021. — 267 p. — ISBN 9813348216.This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.An Introduction to Maximal Regularity for Parabolic Evolution Equations
On Stability and Bifurcation in Parallel Flows of Compressible Navier-Stokes Equations
Uniform Regularity for a Compressible Gross-Pitaevskii-Navier-Stokes System
Singular Limit Problem to the Keller-Segel System in Critical Spaces and Related Medical Problems—An Application of Maximal Regularity
HJB Equation, Dynamic Programming Principle, and Stochastic Optimal Control
Regularity of Solutions of Obstacle Problems –Old & New–
High-Energy Eigenfunctions of the Laplacian on the Torus and the Sphere with Nodal Sets of Complicated Topology