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Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.

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Motivated by the question Relationship between the vortex filament equation and the cubic Schrödinger equation, I'd like to ask the following: Where can I find a reference on wellposedness results …
asked May 16 '19 by Kei
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How is the vortex filament equation $$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$ where $\chi(t,s)$ is a curve in $\mathbb R^3$, related to the cubic Schrödinger equation? Note …
asked May 15 '19 by Kei
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Let us consider the vortex filament equation $$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$ where $\chi(t,s)$ is a curve in $\mathbb R^3$. How is the Cauchy problem for the vort …
asked May 15 '19 by Kei
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It is well known that the initial-value problem for the wave equation on $\mathbb R^N$ can be studied by means of Fourier transform. What reference presents well-posedness results and qualitative pro …
asked May 19 '19 by Kei
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Where can I find surveys on the mathematical aspects of the vortex filament equation? In particular, I'm interested in the following topics: physical motivation; notion of solutions and wellposedn …
asked May 14 '19 by Kei