共查询到20条相似文献,搜索用时 15 毫秒
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Pedro Isaza 《Journal of Differential Equations》2006,230(2):661-681
In this article we consider the initial value problem for the Ostrovsky equation:
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Pedro Isaza 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4016-4029
In this paper we prove that sufficiently smooth solutions of the Ostrovsky equation with positive dispersion,
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Pedro Isaza 《Journal of Differential Equations》2009,247(6):1851-4029
In this article we prove that sufficiently smooth solutions of the Ostrovsky equation with negative dispersion:
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In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation:
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We make use of the method of modulus of continuity [A. Kiselev, F. Nazarov, R. Shterenberg, Blow up and regularity for fractal Burgers equation, Dyn. Partial Differ. Equ. 5 (2008) 211-240] and Fourier localization technique [H. Abidi, T. Hmidi, On the global well-posedness of the critical quasi-geostrophic equation, SIAM J. Math. Anal. 40 (1) (2008) 167-185] [H. Abidi, T. Hmidi, On the global well-posedness of the critical quasi-geostrophic equation, SIAM J. Math. Anal. 40 (1) (2008) 167-185] to prove the global well-posedness of the critical Burgers equation t∂u+ux∂u+Λu=0 in critical Besov spaces with p∈[1,∞), where . 相似文献
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In this paper we establish a new bilinear estimate in suitable Bourgain spaces by using a fundamental estimate on dyadic blocks for the Kawahara equation which was obtained by the [k;Z] multiplier norm method of Tao (2001) [2]; then the local well-posedness of the Cauchy problem for a fifth-order shallow water wave equation in with is obtained by the Fourier restriction norm method. And some ill-posedness in with is derived from a general principle of Bejenaru and Tao. 相似文献
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David Karapetyan 《Journal of Differential Equations》2010,249(4):796-826
It is shown that the solution map for the hyperelastic rod equation is not uniformly continuous on bounded sets of Sobolev spaces with exponent greater than 3/2 in the periodic case and greater than 1 in the non-periodic case. The proof is based on the method of approximate solutions and well-posedness estimates for the solution and its lifespan. 相似文献
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Having the ill-posedness in the range s<−3/4 of the Cauchy problem for the Benjamin equation with an initial Hs(R) data, we prove that the already-established local well-posedness in the range s>−3/4 of this initial value problem is extendable to s=−3/4 and also that such a well-posed property is globally valid for s∈[−3/4,∞). 相似文献
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Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation
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Yongsheng Li 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1610-1625
In this paper we consider the initial value problem of the Benjamin equation
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Soonsik Kwon 《Journal of Differential Equations》2008,245(9):2627-2659
In this paper we prove that the following fifth-order equation arising from the KdV hierarchy
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Mariano De Leo 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):979-986
This paper is concerned with the existence of ground states for the Schrödinger-Poisson equation , where V(u) is a Hartree type nonlinearity, stemming from the coupling with the Poisson equation, which includes the so-called doping profile or impurities. By means of variational methods in the energy space we show that ground states exist and belong to the Schwartz space of rapidly decreasing functions whenever total charge not exceed some critical value, it is also shown that for values of the total charge greater than this critical value, energy is not bounded from below. In addition, we show that this critical value is the total charge given by the impurities. 相似文献
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The local well-posedness for the generalized two-dimensional (2D) Ginzburg-Landau equation is obtained for initial data in Hs(R2)(s>1/2). The global result is also obtained in Hs(R2)(s>1/2) under some conditions. The results on local and global well-posedness are sharp except the endpoint s=1/2. We mainly use the Tao's [k;Z]-multiplier method to obtain the trilinear and multilinear estimates. 相似文献
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By using the I-method, we prove that the Cauchy problem of the fifth-order shallow water equation is globally well-posed in the Sobolev space Hs(R) provided . 相似文献
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In this paper we prove the local-in-time well-posedness for the 2D non-dissipative quasi-geostrophic equation, and study the blow-up criterion in the critical Besov spaces. These results improve the previous one by Constantin et al. [P. Constantin, A. Majda, E. Tabak, Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar, Nonlinearity 7 (1994) 1495–1533]. 相似文献
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Kotaro Tsugawa 《Journal of Differential Equations》2009,247(12):3163-3815
We consider the Cauchy problem of the Ostrovsky equation. We first prove the time local well-posedness in the anisotropic Sobolev space Hs,a with s>−a/2−3/4 and 0?a?−1 by the Fourier restriction norm method. This result include the time local well-posedness in Hs with s>−3/4 for both positive and negative dissipation, namely for both βγ>0 and βγ<0. We next consider the weak rotation limit. We prove that the solution of the Ostrovsky equation converges to the solution of the KdV equation when the rotation parameter γ goes to 0 and the initial data of the KdV equation is in L2. To show this result, we prove a bilinear estimate which is uniform with respect to γ. 相似文献
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Xingyu Yang 《Journal of Differential Equations》2010,248(6):1458-1472
The Cauchy problem of a fifth-order shallow water equation