共查询到20条相似文献，搜索用时 38 毫秒
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This paper determines the existence of a unique local solution for the 3D generalized magnetohydrodynamics equations. In order to be more precise, our solution is obtained by involving Lei–Lin–Gevrey spaces as well as Lei–Lin spaces. Furthermore, we present five new blow-up criteria for this same system when the maximal time of existence is finite. It is important to point out that one of these criteria is obtained by assuming fractional Laplacians with equal powers. 相似文献
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We prove the existence of global weak solution of the two‐dimensional dissipative quasi‐geostrophic equations with small initial data in and local well‐posedness with the large initial data in the same space. Our proof is based on constructing a commutator related to the problem, as well as its estimate. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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This paper concerns the threshold of global existence and finite time blow up of solutions to the time-dependent focusing Gross-Pitaevskii equation describing the Bose-Einstein condensation of trapped dipolar quantum gases. Via a construction of new cross-constrained invariant sets, it is shown that either the corresponding solution globally exists or blows up in finite time according to some appropriate assumptions about the initial datum. 相似文献
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本文考虑了一类具有强阻尼和非线性阻尼项的波动方程:utt, - △u - ω△u1, +μ | u1|m-2 u1 =| u |p-2 u,其中P>2,m>2,w=μ1.利用变分法和紧性引理,本文证明了基态驻波解的存在性.并且得到了解的整体存在和爆破条件. 相似文献
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We consider the nonlocal coupled parabolic system
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Salim A. Messaoudi 《Journal of Mathematical Analysis and Applications》2010,365(1):277-83
This work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy. 相似文献
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We study a type of nonlinear parabolic equations. In terms of the variational characterization of the corresponding nonlinear elliptic equations and the invariant flow arguments, we establish the sharp criteria for global existence and blow-up. Furthermore, we also get the instability of the steady states and the global existence with small initial data. 相似文献
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The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions. 相似文献
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The authors consider the critical exponent problem for the variable coefficients wave equation with a space dependent potential and source term. For sufficiently small data with compact support, if the power of nonlinearity is larger than the expected exponent, it is proved that there exists a global solution. Furthermore, the precise decay estimates for the energy, L2 and Lp+1 norms of solutions are also established. In addition, the blow-up of the solutions is proved for arbitrary initial data with compact support when the power of nonlinearity is less than some constant. 相似文献
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T. Tachim Medjo 《Numerical Methods for Partial Differential Equations》1999,15(4):489-502
In this article, we propose a mixed variational formulation for the streamfunction vorticity potential form for the two‐layer quasi‐geostrophic model of the ocean. We prove the existence and uniqueness of solutions of the mixed variational problem. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 489–502, 1999 相似文献
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We prove necessary and sufficient conditions for global in time existence of solutions of ordinary differential equations on infinite dimensional Banach spaces and manifolds under some natural additional hypotheses, in particular, for equations with right-hand sides, given on everywhere dense subsets of phase spaces. 相似文献
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In this paper, we prove two results about the blow‐up criterion of the three‐dimensional incompressible Navier‐Stokes equation in the Sobolev space . The first one improves the result of Cortissoz et al. The second deals with the relationship of the blow up in and some critical spaces. Fourier analysis and standard techniques are used. 相似文献
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In this work, we consider a nonlinear coupled wave equations with initial‐boundary value conditions and nonlinear damping and source terms. Under suitable assumptions on the damping terms and source terms and initial data in the stable set, we obtain that the decay estimates of the energy function is exponential or polynomial by using Nakao's method. By using the energy method, we obtain the blow‐up result of solution with some positive or nonpositive initial energy. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Yuzhao Wang 《偏微分方程通讯》2013,38(10):1694-1722
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In this paper we study well‐posedness of the damped nonlinear wave equation in Ω × (0, ∞) with initial and Dirichlet boundary condition, where Ω is a bounded domain in ?2; ω?0, ωλ1+µ>0 with λ1 being the first eigenvalue of ?Δ under zero boundary condition. Under the assumptions that g(·) is a function with exponential growth at the infinity and the initial data lie in some suitable sets we establish several results concerning local existence, global existence, uniqueness and finite time blow‐up property and uniform decay estimates of the energy. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献