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I am in serious need of an English translation for the following paper:

Séminaire Bourbaki by Jean Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace, d'après Bourgain, Astérisque 1996, Numdam free access.

I searched a lot before I posted this request. I appreciate any help.

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    $\begingroup$ Is there a reason to believe that such a translation exists? Otherwise, you just have to find someone to translate if for you (knowing the language is usually not enough, one would need to understand the math), or read it yourself. $\endgroup$
    – Jukka Kohonen
    Commented Jan 22, 2023 at 14:41
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    $\begingroup$ Running it through google translate is probably quickest and certainly cheapest. The translation won't be perfect (mostly due to direct translations of the math terminology), but from context you would be able to easily fill in those gaps. $\endgroup$
    – Aleksandar Milivojević
    Commented Jan 22, 2023 at 14:50
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    $\begingroup$ I do not think Séminaire Bourbaki is systematically translated into English (long ago there used to be efforts of translating into Russian but the last translated year was 1992, I believe), so it would be just pure chance if such a translation exists. I concur with Aleksandar and Ben : an automatic translation (probably DeepL will be a bit more efficient) is something you can easily do by yourself, and it will serve most imaginable purposes. $\endgroup$
    – Vladimir Dotsenko
    Commented Jan 22, 2023 at 15:47
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    $\begingroup$ Is there any particular reason to read Ginibre's summary, as opposed to Bourgain's original papers (which were in English)? (For example, if you have a specific reference to a specific portion of the report, some kind soul may be willing to translate a few pages for you. Certainly 26 pages is too much.) $\endgroup$
    – Willie Wong
    Commented Jan 22, 2023 at 20:52
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    $\begingroup$ @Mr.Proof The Bourbaki Seminar is usually a report by a third party on some recent "hot" development in the field, which provides additional context / exposition / introduction. It is often a great way to get an overview (if you speak/read French). I think of it more like a "Journal Club on Steroids". $\endgroup$
    – Willie Wong
    Commented Jan 23, 2023 at 2:32

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Here is a randomly selected paragraph, translated using DeepL in less than a second, and then a little TeX for the equations, under 15 seconds work:

The Cauchy problem for these equations (at least for SNL and KdVG) is fairly well understood in $\mathbb{R}^n$ (see [C], [KPV2] and their bibliography). It can be be studied in the following way. The equation is of the type: $\partial_t u=Lu+f_0(u)$ where $L$ is a linear anti-self-adjoint operator in a Hilbert space $H$, typically $L^2$ or a Sobolev space $H^S$, and generates a unitary group with one parameter $U(t)=\exp(tL)$ in $H$. The Cauchy problem for equation (1.6) with initial data $u(t=0) = \varphi\in H$ is then equivalent to the integral equation: ... where the notation $*_R$ denotes the time-delayed convolution (delayed referring to the fact that

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  • $\begingroup$ Thank you very much. But it is not a better idea to rely on DeepL when one has serous work. $\endgroup$
    – Mr. Proof
    Commented Jan 22, 2023 at 22:55
  • $\begingroup$ I wouldn't know about serious work. Just look at my hat! $\endgroup$
    – Ben McKay
    Commented Jan 23, 2023 at 12:16

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