# PDEs on torus $\mathbb T$

(Hope this question is o.k. for MO)

I have been learning PDE(non linear dispersive equations) techniques, mainly using harmonic analysis(kind of Strichartz estimates, estimates for unimodular Fourier multiplier); to solve it.

But mainly with underlying framework function spaces, which I have seen so far, are functions/distributions on $$\mathbb R^{n}.$$ (For instance,Sobolev spaces $$H^{s}(\mathbb R^{n})$$, Besove spaces $$B^{p,q}(\mathbb R^{n})$$, Modulation spaces $$M^{p,q}(\mathbb R^{n})$$, etc..)

My Question is: Bit vague:How the theory had gone(or have been going), if one consider the underlying framework function spaces on torus $$\mathbb T$$ (for instance $$H^{s}(\mathbb T)$$, $$A(\mathbb T)$$, etc...) ? Is there something common in handling the non linear dispersive equations on compact group $$\mathbb T$$ and on group $$\mathbb R$$ ?

What are the reference (book/ recent monograph/ fundamental papers) for the study of non linear dispersive equations on torus $$\mathbb T$$ ?