Existence of solutions to fluid equations in Hölder and uniformly local Sobolev spaces (Q6041815)
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scientific article; zbMATH DE number 7686109
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of solutions to fluid equations in Hölder and uniformly local Sobolev spaces |
scientific article; zbMATH DE number 7686109 |
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Existence of solutions to fluid equations in Hölder and uniformly local Sobolev spaces (English)
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15 May 2023
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The authors show short-time existence of solutions to the surface quasi-geostrophic (SQG) equation in suitable Hölder spaces and also existence of solutions of SQG in another class of non-decaying functions, namely the uniformly local Sobolev space. In the appendices, they establish Serfati-like identities for SQG and 3D Euler equations, a constitutive relation for SQG, and a pressure identity for 3D Euler equations akin to ones used in 2D.
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three-dimensional Euler equations
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short-time existence
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surface quasi-geostrophic equation
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Serfati identity
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pressure identity
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