Tohru Ozawa – författare

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications.

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers.  The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations.

Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations.

This volume is edited as the proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) "The Role of Metrics in the Theory of Partial Differential Equations", held for the period of July 2-13, 2018 in Hokkaido University, Sapporo, Japan. This volume consists of peer-reviewed articles written by speakers who actively lead the fields of partial differential equations, numerical analysis, harmonic analysis, and geometric analysis. It should be underlined that 3 survey articles provided by course lecturers show an interesting direction of analysis under various metrics. This volume is suitable for any graduate students and young researchers to motivate the research on these fields from the viewpoint of metrics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

This book presents the proceedings of the Minisymposium “Various Methods for the Analysis of PDEs” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. This volume brings together a diverse group of researchers, practitioners, and experts who have shared their latest developments and innovations in the field of Partial Differential Equations (PDEs).The papers included in this volume reflect the high quality and breadth of research presented at the session. Covering a wide range of topics, this collection showcases the dynamic and interdisciplinary nature of the Analysis of PDEs. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of academic excellence.Key topics include:Interpolation Inequalities: Novel contributions to the field, including stability results for the Sobolev inequality and the Gaussian logarithmic Sobolev inequality with explicit and dimensionally sharp constants.Strichartz Estimates: New estimates specifically for orthonormal families of initial data, extending traditional Strichartz estimates to provide deeper insights into the behavior of solutions to dispersive equations, including the wave equation, Klein-Gordon equation, and fractional Schrödinger equations.Asymptotic Behavior: Detailed analysis of the asymptotic behavior for the massive Maxwell–Klein–Gordon system under the Lorenz gauge condition in dimension (1+4), including scattering results.Time-Dependent Free Schrödinger Operator: A new characterization of this operator, highlighting its unique invariance under the Galilei group in Euclidean space-time.Lifespan Estimates: Analysis of the lifespan of solutions to the damped wave equation, with decay estimates for particular initial data in the case of nonlinearity with subcritical Fujita exponent.This book aims to provide readers with a profound and cohesive understanding of the current state of splitting optimization while inspiring future research and innovation in this dynamic field.

This book presents the proceedings of the Minisymposium “Various Methods for the Analysis of PDEs” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. This volume brings together a diverse group of researchers, practitioners, and experts who have shared their latest developments and innovations in the field of Partial Differential Equations (PDEs).The papers included in this volume reflect the high quality and breadth of research presented at the session. Covering a wide range of topics, this collection showcases the dynamic and interdisciplinary nature of the Analysis of PDEs. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of academic excellence.Key topics include:Interpolation Inequalities: Novel contributions to the field, including stability results for the Sobolev inequality and the Gaussian logarithmic Sobolev inequality with explicit and dimensionally sharp constants.Strichartz Estimates: New estimates specifically for orthonormal families of initial data, extending traditional Strichartz estimates to provide deeper insights into the behavior of solutions to dispersive equations, including the wave equation, Klein-Gordon equation, and fractional Schrödinger equations.Asymptotic Behavior: Detailed analysis of the asymptotic behavior for the massive Maxwell–Klein–Gordon system under the Lorenz gauge condition in dimension (1+4), including scattering results.Time-Dependent Free Schrödinger Operator: A new characterization of this operator, highlighting its unique invariance under the Galilei group in Euclidean space-time.Lifespan Estimates: Analysis of the lifespan of solutions to the damped wave equation, with decay estimates for particular initial data in the case of nonlinearity with subcritical Fujita exponent.This book aims to provide readers with a profound and cohesive understanding of the current state of splitting optimization while inspiring future research and innovation in this dynamic field.