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arXiv · 2511.01117

The analytic method of constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces

I. Kukavica·W. S. Ożański
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Abstract

We introduce a new method for constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces on an arbitrary Sobolev bounded domain. The method is based on a construction of an analytic solution in an analytically approximated domain, after which we apply analytic persistence to extend the analytic solution using given a priori bounds in Sobolev spaces. The method does not introduce any modification or regularization of the equations themselves and appears applicable to many other PDEs.

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I. Kukavica, W. S. Ożański. 2025-11-02. The analytic method of constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces. https://arxiv.org/abs/2511.01117

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