skip to content
HARMONIC ANALYSIS METHOD FOR NONLINEAR EVOLUTION EQUATIONS, I Preview this item
ClosePreview this item
Checking...

HARMONIC ANALYSIS METHOD FOR NONLINEAR EVOLUTION EQUATIONS, I

Author: Baoxiang Wang; Zhaohui Huo; Chengchun Hao
Publisher: Singapore : World Scientific Publishing Company, 2011.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Wang, Baoxiang.
HARMONIC ANALYSIS METHOD FOR NONLINEAR EVOLUTION EQUATIONS, I.
Singapore : World Scientific Publishing Company, ©2011
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Baoxiang Wang; Zhaohui Huo; Chengchun Hao
ISBN: 9789814360746 9814360740
OCLC Number: 877767902
Notes: 8.2 Basic surgery tools for the Boltzmann operator.
Description: 1 online resource (298 pages)
Contents: Preface; Contents; 1. Fourier multiplier, function space X; 1.1 Schwartz space, tempered distribution, Fourier transform; 1.2 Fourier multiplier on L; 1.3 Dyadic decomposition, Besov and Triebel spaces; 1.4 Embeddings on X; 1.5 Differential-difference norm on X; 1.6 Homogeneous space; 1.7 Bessel (Riesz) potential spaces H (H); 1.8 Fractional Gagliardo-Nirenberg inequalities; 1.8.1 GN inequality in; 1.8.2 GN inequality in; 2. Navier-Stokes equation; 2.1 Introduction; 2.1.1 Model, energy structure; 2.1.2 Equivalent form of NS; 2.1.3 Critical spaces. 2.2 Time-space estimates for the heat semi-group2.2.1 L L estimate for the heat semi-group; 2.2.2 Time-space estimates for the heat semi-group; 2.3 Global well-posedness in L of NS in 2D; 2.4 Well-posedness in L of NS in higher dimensions; 2.5 Regularity of solutions for NS; 2.5.1 Gevrey class and function space E; 2.5.2 Estimates of heat semi-group in E; 2.5.3 Bilinear estimates in E; 2.5.4 Gevrey regularity of NS equation; 3. Strichartz estimates for linear dispersive equations; 3.1 L ' L estimates for the dispersive semi-group; 3.2 Strichartz inequalities: dual estimate techniques. 3.3 Strichartz estimates at endpoints4. Local and global wellposedness for nonlinear dispersive equations; 4.1 Why is the Strichartz estimate useful; 4.2 Nonlinear mapping estimates in Besov spaces; 4.3 Critical and subcritical NLS in H; 4.3.1 Critical NLS in H; 4.3.2 Wellposedness in H; 4.4 Global wellposedness of NLS in L and H; 4.5 Critical and subcritical NLKG in H; 5. The low regularity theory for the nonlinear dispersive equations; 5.1 Bourgain space; 5.2 Local smoothing effect and maximal function estimates; 5.3 Bilinear estimates for KdV and local well-posedness. 5.4 Local well-posedness for KdV in H5.5 I-method; 5.6 Schrödinger equation with derivative; 5.7 Some other dispersive equations; 6. Frequency-uniform decomposition techniques; 6.1 Why does the frequency-uniform decomposition work; 6.2 Frequency-uniform decomposition, modulation spaces; 6.2.1 Basic properties on modulation spaces; 6.3 Inclusions between Besov and modulation spaces; 6.4 NLS and NLKG in modulation spaces; 6.4.1 Schrödinger and Klein-Gordon semigroup in modulation spaces; 6.4.2 Strichartz estimates in modulation spaces; 6.4.3 Wellposedness for NLS and NLKG. 6.5 Derivative nonlinear Schrödinger equations6.5.1 Global linear estimates; 6.5.2 Frequency-localized linear estimates; 6.5.3 Proof of global wellposedness for small rough data; 7. Conservations, Morawetz' estimates of nonlinear Schrödinger equations; 7.1 Nöther's theorem; 7.2 Invariance and conservation law; 7.3 Virial identity and Morawetz inequality; 7.4 Morawetz' interaction inequality; 7.5 Scattering results for NLS; 8. Boltzmann equation without angular cutoff; 8.1 Models for collisions in kinetic theory; 8.1.1 Transport model; 8.1.2 Boltzmann model; 8.1.3 Cross section.

Abstract:

This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


<http://www.worldcat.org/oclc/877767902>
library:oclcnum"877767902"
library:placeOfPublication
library:placeOfPublication
rdf:typeschema:MediaObject
rdf:typeschema:Book
rdf:valueUnknown value: dct
schema:about
schema:about
schema:about
schema:about
schema:bookFormatschema:EBook
schema:contributor
schema:contributor
schema:creator
schema:datePublished"2011"
schema:description"Preface; Contents; 1. Fourier multiplier, function space X; 1.1 Schwartz space, tempered distribution, Fourier transform; 1.2 Fourier multiplier on L; 1.3 Dyadic decomposition, Besov and Triebel spaces; 1.4 Embeddings on X; 1.5 Differential-difference norm on X; 1.6 Homogeneous space; 1.7 Bessel (Riesz) potential spaces H (H); 1.8 Fractional Gagliardo-Nirenberg inequalities; 1.8.1 GN inequality in; 1.8.2 GN inequality in; 2. Navier-Stokes equation; 2.1 Introduction; 2.1.1 Model, energy structure; 2.1.2 Equivalent form of NS; 2.1.3 Critical spaces."@en
schema:description"This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students."@en
schema:exampleOfWork<http://worldcat.org/entity/work/id/1028346618>
schema:genre"Electronic books"@en
schema:inLanguage"en"
schema:name"HARMONIC ANALYSIS METHOD FOR NONLINEAR EVOLUTION EQUATIONS, I"@en
schema:publication
schema:publisher
schema:url<http://public.eblib.com/choice/publicfullrecord.aspx?p=840682>
schema:workExample
wdrs:describedby

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.