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On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation

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  • In this article, we provide the uniform $H^2$-regularity results with respect to $t$ of the solution and its time derivatives for the 2D Cahn-Hilliard equation. Based on sharp a priori estimates for the solution of problem under the assumption on the initial value, we show that the $H^2$-regularity of the solution and its first and second order time derivatives only depend on $\epsilon^{-1}$.
    Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35Q35, 37L, 82C26.

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