An improved global well-posedness result for the modified Zakharov equations in 1-D
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
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 ion-acoustic waves is studied. In this paper, it is proven that the system is globally well-posed in $(u,n)\in L^2\times L^2$ by making use of Bourgain restriction norm method and $L^2$ 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 \cite{GZG} to lower regularity.
Abstract
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 ion-acoustic waves is studied. In this paper, it is proven that the system is globally well-posed in $(u,n)\in L^2\times L^2$ by making use of Bourgain restriction norm method and $L^2$ 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 \cite{GZG} to lower regularity.
참고문헌 (18)
- Ioan Bejenaru, "Convolutions of singular measures and applications to the Zakharov system", Journal of Functional Analysis, 261(2), pp.478~506 (2011), Elsevier BV[DOI]
- I Bejenaru, "On the 2D Zakharov system with L2-Schrodinger data", Nonlinearity, 22(5), pp.1063~1089 (2009), IOP Publishing[DOI]
- J. Bourgain, "Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations", Geometric and Functional Analysis, 3(2), pp.107~156 (1993), Springer Science and Business Media LLC[DOI]
- Igor Chueshov, "Quantum Zakharov model in a bounded domain", Zeitschrift für angewandte Mathematik und Physik, 64(4), pp.967~989 (2012), Springer Science and Business Media LLC[DOI]
- James Colliander, "Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems", Transactions of the American Mathematical Society, 360(09), pp.4619~4638 (2008), American Mathematical Society (AMS)[DOI]
- Shao-mei Fang, "Existence of weak solution for quantum Zakharov equations for plasmas model", Applied Mathematics and Mechanics, 32(10), pp.1339~1344 (2011), Springer Science and Business Media LLC[DOI]
- L. G. Garcia, "Modied Zakharov equations for plasmas with a quantum correction", Phys. Plasmas, 12, pp.012302~ (2005)
- J. Ginibre, "On the Cauchy Problem for the Zakharov System", Journal of Functional Analysis, 151(2), pp.384~436 (1997), Elsevier BV[DOI]
- Yanfeng Guo, "Global well-posedness and the classical limit of the solution for the quantum Zakharov system", Zeitschrift für angewandte Mathematik und Physik, 64(1), pp.53~68 (2012), Springer Science and Business Media LLC[DOI]
- F. Haas, "Variational approach for the quantum Zakharov system", Phys. Plasmas, 14, pp.042309~ (2007)
- F. Haas, "Quantum plasmas" (2011), Springer
- F. Haas, "Quantum and classical dynamics of Langmuir wave packets", Phys. Rev. E, 79, pp.066402~ (2009)
- Carlos Kenig, "Oscillatory integrals and regularity of dispersive equations", Indiana University Mathematics Journal, 40(1), pp.33~ (1991), Indiana University Mathematics Journal[DOI]
- Nader Masmoudi, "Energy convergence for singular limits of Zakharov type systems", Inventiones mathematicae, 172(3), pp.535~583 (2008), Springer Science and Business Media LLC[DOI]
- Hartmut Pecher, "An improved local well-posedness result for the one-dimensional Zakharov system", Journal of Mathematical Analysis and Applications, 342(2), pp.1440~1454 (2008), Elsevier BV[DOI]
- T. Tao, "Nonlinear dispersive equations" (2006), Published for the Conference Board of the Mathematical Sciences
- Shujun You, "Global solution for quantum Zakharov equations", Applied Mathematics and Mechanics, 38(4), pp.603~616 (2016), Springer Science and Business Media LLC[DOI]
- You Shujun, "Initial boundary value problem for modified Zakharov equations", Acta Mathematica Scientia, 32(4), pp.1455~1466 (2012), Elsevier BV[DOI]