Global well-posedness of NLS equations

dc.contributor	Graduate Program in Mathematics.
dc.contributor.advisor	Gürel, Burak.
dc.contributor.author	Yılmaz, Oğuz.
dc.date.accessioned	2023-10-15T11:13:22Z
dc.date.available	2023-10-15T11:13:22Z
dc.date.issued	2022
dc.identifier.other	MATH 2022 Y56
dc.identifier.uri	http://digitalarchive.boun.edu.tr/handle/123456789/19901
dc.description.abstract	The thesis is a survey of the I-method. After introducing the method, we discuss the implementation of this method to cubic, defocusing nonlinear Schrödinger equation in the spatial dimension n = 2 and quintic, defocusing nonlinear Schr¨odinger equation in the spatial dimension n = 1 with detailed calculations. We will find out on which type of equations one can use the I-method. We then mention our joint work with Engin Ba¸sako˘glu on the cubic defocusing fourth order nonlinear Schr¨odinger equation in the spatial dimension n = 4. Lastly, we discuss advantage and disadvantage of the method and share our idea of a study plan of the same equation in the spatial dimensions n = 2, 3 as future work.
dc.publisher	Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022.
dc.subject.lcsh	Schrödinger equation.
dc.title	Global well-posedness of NLS equations
dc.format.pages	ix, 45 leaves