대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권3호
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  • Pages.735-748
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  • 2022
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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AN IMPROVED GLOBAL WELL-POSEDNESS RESULT FOR THE MODIFIED ZAKHAROV EQUATIONS IN 1-D

  • Soenjaya, Agus L. (Pre-University Mathematics Department Merlion School)
  • 투고 : 2021.06.14
  • 심사 : 2021.09.02
  • 발행 : 2022.07.31
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초록

The global well-posedness for the fourth-order modified Zakharov equations in 1-D, which is a system of PDE in two variables describing interactions between quantum Langmuir and quantum ionacoustic waves is studied. In this paper, it is proven that the system is globally well-posed in (u, n) ∈ L2 × L2 by making use of Bourgain restriction norm method and L2 conservation law in u, and controlling the growth of n via appropriate estimates in the local theory. In particular, this improves on the well-posedness results for this system in [9] to lower regularity.

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참고문헌

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