共查询到20条相似文献,搜索用时 1 毫秒
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Takayoshi Ogawa 《Journal of Differential Equations》2003,190(1):39-63
We show that a smooth solution of the 3-D Euler equations in a bounded domain breaks down, if and only if a certain norm of vorticity blows up at the same time. Here this norm is weaker than bmo-norm. 相似文献
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E. M. Vorob'ev 《Acta Appl Math》1991,23(1):1-24
The method of reduction previously known in the theory of Hamiltonian systems with symmetries is developed in order to obtain exact group-invariant solutions of systems of partial differential equations. This method leads to representations of quotient equations which are very convenient for the systematic analysis of invariant solutions of boundary value problems. In the case of partially invariant solutions, necessary and sufficient conditions of their invariance with respect to subalgebras of symmetry algebras are given. The concept of partial symmetries of differential equations is considered. 相似文献
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Jianwei Yang Shu Wang Juan Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7005-7011
The aim of this paper is to study multidimensional Euler–Maxwell equations for plasmas with short momentum relaxation time. The convergence for the smooth solutions to the compressible Euler–Maxwell equations toward the solutions to the smooth solutions to the drift–diffusion equations is proved by means of the Maxwell iteration, as the relaxation time tends to zero. Meanwhile, the formal derivation of the latter from the former is justified. 相似文献
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E. M. Vorob'ev 《Acta Appl Math》1992,26(1):61-86
When symmetries of differential equations are applied, various types of associated systems of equations appear. Compatibility conditions of the associated systems expressed in the form of differential equations inherit Lie symmetries of the initial equations. Invariant solutions to compatibility systems are known as orbits of partially invariant and generic solutions involved in the Lie group foliation of differential equations and so on. In some cases Bäcklund transformations and differential substitutions connecting quotient equations for compatibility conditions and initial systems naturally arise. Besides, Ovsiannikov's orbit method for finding partially invariant solutions is essentially based on such symmetries. 相似文献
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Donatella Donatelli 《Journal of Differential Equations》2008,245(5):1356-1385
A model for the dynamics of gaseous stars is introduced and formulated by the Navier-Stokes-Poisson system for compressible, reacting gases. The combined quasineutral and inviscid limit of the Navier-Stokes-Poisson system in the torus Tn is investigated. The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations is proven for the global weak solution and for the case of general initial data. 相似文献
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Linghai Zhang 《Journal of Differential Equations》2008,245(11):3470-3502
Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations
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F. Jochmann 《Applicable analysis》2013,92(1-2):199-212
In this paper the long time asymptotic behavior of solutions of Maxwell's equations in a bounded domain is investigated. A possibly nonlinear damping term arising from the electric conductivity is considered, whith vanishes on some part of the domain 相似文献
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The time decay of solutions to nonlinear dispersive equations of the typeMu
t+F(u)x=0 is established using the optimal estimates for the linearized equation and standard techniques from scattering theory. 相似文献
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Xin ZhongXing-Ping Wu Chun-Lei Tang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3829-3848
We introduce Triebel-Lizorkin-Lorentz function spaces, based on the Lorentz Lp,q-spaces instead of the standard Lp-spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of inviscid incompressible fluid in Rn,n≥2. As a corollary we obtain global existence of solutions to the 2D Euler equations in the Triebel-Lizorkin-Lorentz space. For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator estimates in our spaces. The key methods of proof used are the Littlewood-Paley decomposition and the paradifferential calculus by J.M. Bony. 相似文献
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Jun-ichi Segata 《Journal of Differential Equations》2008,245(2):281-306
We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as “Hirota” equation. This equation is a mixture of cubic nonlinear Schrödinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given “modified” free profile by using the two asymptotic formulae for some oscillatory integrals. 相似文献
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We consider the Cauchy problem in Rn for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted L1,1(Rn) data by using a method introduced in [9] and/or [10]. 相似文献
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Yong Zhou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(3):750-766
In this paper, local well-posedness for the density dependent incompressible Euler equations is established in Besov spaces. We also obtain a blow-up criterion for the corresponding solution. 相似文献
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Carsten Blank Martina Chirilus Bruckner Christopher Chong Vincent Lescarret Guido Schneider Hannes Uecker 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(3):554-557
We prove the validity of a technical assumption necessary in a proof of the validity of the nonlinear Schr?dinger equation
as envelope equation in quadratic spatially periodic media.
相似文献
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Lucas C.F. Ferreira 《Journal of Differential Equations》2011,250(4):2045-2063
We study the equation Δu+u|u|p−1+V(x)u+f(x)=0 in Rn, where n?3 and p>n/(n−2). The forcing term f and the potential V can be singular at zero, change sign and decay polynomially at infinity. We can consider anisotropic potentials of form h(x)|x|−2 where h is not purely angular. We obtain solutions u which blow up at the origin and do not belong to any Lebesgue space Lr. Also, u is positive and radial, in case f and V are. Asymptotic stability properties of solutions, their behavior near the singularity, and decay are addressed. 相似文献
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Kurt Busch Guido Schneider Lasha Tkeshelashvili Hannes Uecker 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):905-939
The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media
can approximately be described by solutions of a Nonlinear Schr?dinger equation. Here we prove estimates for the error made
by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall’s inequality. 相似文献
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Dongho Chae 《Journal of Differential Equations》2010,249(3):571-577
We study the dynamics along the particle trajectories for the 3D axisymmetric Euler equations. In particular, by rewriting the system of equations we find that there exists a complex Riccati type of structure in the system on the whole of R3, which generalizes substantially the previous results in [5] (D. Chae, On the blow-up problem for the axisymmetric 3D Euler equations, Nonlinearity 21 (2008) 2053-2060). Using this structure of equations, we deduce the new blow-up criterion that the radial increment of pressure is not consistent with the global regularity of classical solution. We also derive a much more refined version of the Lagrangian dynamics than that of [6] (D. Chae, On the Lagrangian dynamics for the 3D incompressible Euler equations, Comm. Math. Phys. 269 (2) (2007) 557-569) in the case of axisymmetry. 相似文献