Almost sure well-posedness of fractional Schrödinger equations with Hartree nonlinearity (Q1707955)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost sure well-posedness of fractional Schrödinger equations with Hartree nonlinearity |
scientific article |
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Almost sure well-posedness of fractional Schrödinger equations with Hartree nonlinearity (English)
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4 April 2018
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Summary: We consider a Cauchy problem of an energy-critical fractional Schrödinger equation with Hartree nonlinearity below the energy space. Using randomization of functions on \(\mathbb R^d\) associated with the Wiener decomposition, we prove that the Cauchy problem is almost surely locally well posed. Our result includes the Hartree Schrödinger equation (\(\alpha = 2\)).
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nonlinear Schrödinger equation
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fractional Schrödinger equation
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Hartree non-linearity
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almost sure well-posedness
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