Local well posedness of the Euler-Korteweg equations on $\mathbb T^d$

preprint2020arXivOpen access

We consider the Euler-Korteweg system with space periodic boundary conditions $x \in \mathbb T^d$ . We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity assumptions on the initial data.

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Local well posedness of the Euler-Korteweg equations on $\mathbb T^d$

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Local well posedness of the Euler-Korteweg equations on Td \mathbb T^d Td

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Local well posedness of the Euler-Korteweg equations on $\mathbb T^d$