Essays about: "Gustav Jillbratt"

Found 2 essays containing the words Gustav Jillbratt.

1. 1. Steady ideal flows with vorticity in toroidal domains and periodic cylinders

   University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

   Author : Gustav Jillbratt; [2020]
   Keywords : Partial differential equations; Euler equation; Vorticity; Fluid dynamics; Mathematics and Statistics;

   Abstract : In a paper from 1970, Lortz constructs rotational solutions to the steady Euler equation in toroidal domains using a fixed point method. We shall review this method and rewrite it using Banach's fixed point theorem. READ MORE

3. 2. On the variational characterization of quasi-periodic standing waves of the nonlinear Schrödinger equation

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

   Author : Gustav Jillbratt; [2018]
   Keywords : Mathematics and Statistics;

   Abstract : We consider quasi-periodic standing wave solutions U(t, x) = exp(i(ωt−px))Ψ(x) to the one-dimensional defocusing cubic nonlinear Schrödinger equation, where we assume that Ψ : R → C is 2π−periodic. We study a constrained minimization problem associated with these solutions, and we show that solutions with minimal period of Ψ(x) strictly less than 2π cannot be minimizers, whereas locally the minimum is obtained among those solutions with minimal period 2π. READ MORE