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A third-order conservation law for the Kirchhoff-Pokhozhaev equation (2512.12380v1)
Published 13 Dec 2025 in math.AP
Abstract: We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the $L2$-norms of the derivatives up to third order of the solution remain uniformly bounded with respect to time.
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