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Remark on a semirelativistic equation in the energy space

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  • Well-posedness of the Cauchy problem for a semirelativistic equation with cubic nonlinearity is shown in the energy space $H^{1/2}$. Solutions are constructed as a limit of approximation solutions, where the argument on the convergence depends on the completeness of $L^2$ and is independent of compactness. The Yudovitch type argument plays an important role for the convergence arguments.
    Mathematics Subject Classification: Primary: 35Q40; Secondary: 35Q55.


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