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Harmonic analysis method for nonlinear evolution equations, I.

Author: Baoxiang Wang
Publisher: Singapore : World Scientific, 2011.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Document Type: Book
All Authors / Contributors: Baoxiang Wang
ISBN: 9789814360739 9814360732
OCLC Number: 840454885
Description: 283 blz. ; .. cm.
Contents: Machine generated contents note: 1.Fourier multiplier, function space Xp,qs --
1.1.Schwartz space, tempered distribution, Fourier transform --
1.2.Fourier multiplier on Lp --
1.3.Dyadic decomposition, Besov and Triebel spaces --
1.4.Embeddings on Xp,qs --
1.5.Differential-difference norm on Xp,qs --
1.6.Homogeneous space Xp,qs --
1.7.Bessel (Riesz) potential spaces Hps (Hps) --
1.8.Fractional Gagliardo-Nirenberg inequalities --
1.8.1.GN inequality in Bp,qs --
1.8.2.GN inequality in Fp,qs --
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-group --
2.2.1.Lr [] Lp estimate for the heat semi-group --
2.2.2.Time-space estimates for the heat semi-group --
2.3.Global well-posedness in L2 of NS in 2D --
2.4.Well-posedness in Ln of NS in higher dimensions --
2.5.Regularity of solutions for NS --
2.5.1.Gevrey class and function space E2,1s --
2.5.2.Estimates of heat semi-group in E2,1s --
2.5.3.Bilinear estimates in E2,1s --
2.5.4.Gevrey regularity of NS equation --
3.Strichartz estimates for linear dispersive equations --
3.1.Lp' [] Lp estimates for the dispersive semi-group --
3.2.Strichartz inequalities: dual estimate techniques --
3.3.Strichartz estimates at endpoints --
4.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 Hs --
4.3.1.Critical NLS in Hs --
4.3.2.Wellposedness in Hs --
4.4.Global wellposedness of NLS in L2 and H1 --
4.5.Critical and subcritical NLKG in Hs --
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 H-3/4 --
5.5.I-method --
5.6.Schrodinger equation.

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schema:description"Machine generated contents note: 1.Fourier multiplier, function space Xp,qs -- 1.1.Schwartz space, tempered distribution, Fourier transform -- 1.2.Fourier multiplier on Lp -- 1.3.Dyadic decomposition, Besov and Triebel spaces -- 1.4.Embeddings on Xp,qs -- 1.5.Differential-difference norm on Xp,qs -- 1.6.Homogeneous space Xp,qs -- 1.7.Bessel (Riesz) potential spaces Hps (Hps) -- 1.8.Fractional Gagliardo-Nirenberg inequalities -- 1.8.1.GN inequality in Bp,qs -- 1.8.2.GN inequality in Fp,qs -- 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-group -- 2.2.1.Lr [] Lp estimate for the heat semi-group -- 2.2.2.Time-space estimates for the heat semi-group -- 2.3.Global well-posedness in L2 of NS in 2D -- 2.4.Well-posedness in Ln of NS in higher dimensions -- 2.5.Regularity of solutions for NS -- 2.5.1.Gevrey class and function space E2,1s -- 2.5.2.Estimates of heat semi-group in E2,1s -- 2.5.3.Bilinear estimates in E2,1s -- 2.5.4.Gevrey regularity of NS equation -- 3.Strichartz estimates for linear dispersive equations -- 3.1.Lp' [] Lp estimates for the dispersive semi-group -- 3.2.Strichartz inequalities: dual estimate techniques -- 3.3.Strichartz estimates at endpoints -- 4.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 Hs -- 4.3.1.Critical NLS in Hs -- 4.3.2.Wellposedness in Hs -- 4.4.Global wellposedness of NLS in L2 and H1 -- 4.5.Critical and subcritical NLKG in Hs -- 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 H-3/4 -- 5.5.I-method -- 5.6.Schrodinger equation."
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schema:name"Harmonic analysis method for nonlinear evolution equations, I."
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