Cauchy problem for higher-order Schrödinger equations in anisotropic Sobolev space

DOI10.1080/00036810903277127zbMath1179.35309OpenAlexW2052379957WikidataQ58170778 ScholiaQ58170778MaRDI QIDQ3649450

Xiangqing Zhao, Cuihua Guo, Xuemei Wei

Publication date: 4 December 2009

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810903277127

zbMATH Keywords

Cauchy problemlocal well-posednessglobal solvabilitynon-isotropic Schrödinger equationanisotropic Sobolev embedding

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) NLS equations (nonlinear Schrödinger equations) (35Q55) Weak solutions to PDEs (35D30)

Related Items (5)

The global solution of anisotropic fourth-order Schrödinger equation ⋮ Majorant sign of the first order for totally global solvability of a controlled functional operator equation ⋮ Finite dimensional global attractor for a dissipative anisotropic fourth order Schrödinger equation ⋮ Well-posedness of the fourth-order perturbed Schrödinger type equation in non-isotropic Sobolev spaces ⋮ Asymptotic behaviour of the solutions for a weakly damped anisotropic sixth-order Schrödinger type equation in \(\mathbb{R}^2\)

Cites Work

• Pointwise estimates for a class of oscillatory integrals and related \(L^p\)--\(L^q\) estimates
• Strichartz estimates for dispersive equations and solvability of the Kawahara equation
• A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation
• Well-posedness of Cauchy problem of fourth-order Schrödinger equations in anisotropic Sobolev space
• Critical exponents and collapse of nonlinear Schr dinger equations with anisotropic fourth-order dispersion
• Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical Dimension

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