Ebook: Studies in Phase Space Analysis with Applications to PDEs

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important.

Key topics addressed in this volume include:

*general theory of pseudodifferential operators

*Hardy-type inequalities

*linear and non-linear hyperbolic equations and systems

*Schrödinger equations

*water-wave equations

*Euler-Poisson systems

*Navier-Stokes equations

*heat and parabolic equations

Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.

Contributors

T. Alazard P.I. Naumkin

J.-M. Bony F. Nicola

N. Burq T. Nishitani

C. Cazacu T. Okaji

J.-Y. Chemin M. Paicu

E. Cordero A. Parmeggiani

R. Danchin V. Petkov

I. Gallagher M. Reissig

T. Gramchev L. Robbiano

N. Hayashi L. Rodino

J. Huang M. Ruzhanky

D. Lannes J.-C. Saut

F. Linares N. Visciglia

P.B. Mucha P. Zhang

C. Mullaert E. Zuazua

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important.

Key topics addressed in this volume include:

*general theory of pseudodifferential operators

*Hardy-type inequalities

*linear and non-linear hyperbolic equations and systems

*Schr?dinger equations

*water-wave equations

*Euler-Poisson systems

*Navier-Stokes equations

*heat and parabolic equations

Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.

Contributors

T. Alazard P.I. Naumkin

J.-M. Bony F. Nicola

N. Burq T. Nishitani

C. Cazacu T. Okaji

J.-Y. Chemin M. Paicu

E. Cordero A. Parmeggiani

R. Danchin V. Petkov

I. Gallagher M. Reissig

T. Gramchev L. Robbiano

N. Hayashi L. Rodino

J. Huang M. Ruzhanky

D. Lannes J.-C. Saut

F. Linares N. Visciglia

P.B. Mucha P. Zhang

C. Mullaert E. Zuazua

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important.

Key topics addressed in this volume include:

*general theory of pseudodifferential operators

*Hardy-type inequalities

*linear and non-linear hyperbolic equations and systems

*Schr?dinger equations

*water-wave equations

*Euler-Poisson systems

*Navier-Stokes equations

*heat and parabolic equations

Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.

Contributors

T. Alazard P.I. Naumkin

J.-M. Bony F. Nicola

N. Burq T. Nishitani

C. Cazacu T. Okaji

J.-Y. Chemin M. Paicu

E. Cordero A. Parmeggiani

R. Danchin V. Petkov

I. Gallagher M. Reissig

T. Gramchev L. Robbiano

N. Hayashi L. Rodino

J. Huang M. Ruzhanky

D. Lannes J.-C. Saut

F. Linares N. Visciglia

P.B. Mucha P. Zhang

C. Mullaert E. Zuazua

Content:
Front Matter....Pages i-xvii
The Water-Wave Equations: From Zakharov to Euler....Pages 1-20
On the Characterization of Pseudodifferential Operators (Old and New)....Pages 21-34
Improved Multipolar Hardy Inequalities....Pages 35-52
The Role of Spectral Anisotropy in the Resolution of the Three-Dimensional Navier–Stokes Equations....Pages 53-79
Schr?dinger Equations in Modulation Spaces....Pages 81-99
New Maximal Regularity Results for the Heat Equation in Exterior Domains, and Applications....Pages 101-128
Cauchy Problem for Some 2 ? 2 Hyperbolic Systems of Pseudo-differential Equations with Nondiagonalisable Principal Part....Pages 129-145
Scattering Problem for Quadratic Nonlinear Klein–Gordon Equation in 2D....Pages 147-158
Global Solutions to the 3-D Incompressible Inhomogeneous Navier–Stokes System with Rough Density....Pages 159-180
The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation....Pages 181-213
L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models....Pages 215-258
On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case....Pages 259-290
A Note on Unique Continuation for Parabolic Operators with Singular Potentials....Pages 291-312
On the Problem of Positivity of Pseudodifferential Systems....Pages 313-335
Scattering Problems for Symmetric Systems with Dissipative Boundary Conditions....Pages 337-353
Kato Smoothing Effect for Schr?dinger Operator....Pages 355-369
On the Cauchy Problem for NLS with Randomized Initial Data....Pages 371-379

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important.

Key topics addressed in this volume include:

*general theory of pseudodifferential operators

*Hardy-type inequalities

*linear and non-linear hyperbolic equations and systems

*Schr?dinger equations

*water-wave equations

*Euler-Poisson systems

*Navier-Stokes equations

*heat and parabolic equations

Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.

Contributors

T. Alazard P.I. Naumkin

J.-M. Bony F. Nicola

N. Burq T. Nishitani

C. Cazacu T. Okaji

J.-Y. Chemin M. Paicu

E. Cordero A. Parmeggiani

R. Danchin V. Petkov

I. Gallagher M. Reissig

T. Gramchev L. Robbiano

N. Hayashi L. Rodino

J. Huang M. Ruzhanky

D. Lannes J.-C. Saut

F. Linares N. Visciglia

P.B. Mucha P. Zhang

C. Mullaert E. Zuazua

Content:
Front Matter....Pages i-xvii
The Water-Wave Equations: From Zakharov to Euler....Pages 1-20
On the Characterization of Pseudodifferential Operators (Old and New)....Pages 21-34
Improved Multipolar Hardy Inequalities....Pages 35-52
The Role of Spectral Anisotropy in the Resolution of the Three-Dimensional Navier–Stokes Equations....Pages 53-79
Schr?dinger Equations in Modulation Spaces....Pages 81-99
New Maximal Regularity Results for the Heat Equation in Exterior Domains, and Applications....Pages 101-128
Cauchy Problem for Some 2 ? 2 Hyperbolic Systems of Pseudo-differential Equations with Nondiagonalisable Principal Part....Pages 129-145
Scattering Problem for Quadratic Nonlinear Klein–Gordon Equation in 2D....Pages 147-158
Global Solutions to the 3-D Incompressible Inhomogeneous Navier–Stokes System with Rough Density....Pages 159-180
The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation....Pages 181-213
L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models....Pages 215-258
On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case....Pages 259-290
A Note on Unique Continuation for Parabolic Operators with Singular Potentials....Pages 291-312
On the Problem of Positivity of Pseudodifferential Systems....Pages 313-335
Scattering Problems for Symmetric Systems with Dissipative Boundary Conditions....Pages 337-353
Kato Smoothing Effect for Schr?dinger Operator....Pages 355-369
On the Cauchy Problem for NLS with Randomized Initial Data....Pages 371-379
....