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Creators/Authors contains: "Kiselev, Alexander"

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  1. ; (, Nonlinearity)
    Abstract We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdoba–Córdoba–Fontelos (CCF) equation. We discuss how this modification of the CCF equation can be regarded as a reasonable model for solutions to the IPM equation. Working in the class of bounded smooth periodic data, we then show local well-posedness for the 1D IPM model as well as finite time blow-up for a class of initial data. 
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    Free, publicly-accessible full text available April 29, 2026
  2. ; (, Communications on Pure and Applied Mathematics)
    Abstract We consider the patch problem for the ‐(surface quasi‐geostrophic) SQG system with the values and being the 2D Euler and the SQG equations respectively. It is well‐known that the Euler patches are globally wellposed in non‐endpoint Hölder spaces, as well as in , spaces. In stark contrast to the Euler case, we prove that for , the ‐SQG patch problem is strongly illposed ineveryHölder space with . Moreover, in a suitable range of regularity, the same strong illposedness holds foreverySobolev space unless . 
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    Free, publicly-accessible full text available April 1, 2026
  3. ; ; (, Geometric and Functional Analysis)
    Free, publicly-accessible full text available February 13, 2026
  4. ; ; (, Analysis & PDE)
    Free, publicly-accessible full text available January 1, 2026
  5. ; (, Journal of Functional Analysis)
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  6. ; (, Journal of Biological Dynamics)
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  7. ; (, Archive for Rational Mechanics and Analysis)
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  8. ; ; ; (, Journal of the European Mathematical Society)
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  9. ; (, Journal of Nonlinear Science)
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  10. ; (, Archive for Rational Mechanics and Analysis)
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