共查询到20条相似文献,搜索用时 10 毫秒
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In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established. 相似文献
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In this paper, we consider the 2D incompressible generalized Boussinesq system with the general supercritical dissipation. Using the Fourier localization method, we obtain the local and global well-posedness for the system, and give some blow-up criterion with the velocity or the temperature. 相似文献
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In this paper, we study the 3D compressible magnetohydrodynamic equations. We obtain a blow up criterion for the local strong solutions just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion (see J.T. Beal, T. Kato and A. Majda (1984) [1]) for the ideal incompressible flow. In addition, initial vacuum is allowed in our case. 相似文献
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Daoyuan Fang Ruizhao Zi Ting Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3130-3141
We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is allowed. 相似文献
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This paper proves two regularity criteria for the density-dependent Hall-MHD system with positive initial density. We also prove a global nonexistence result for initial density with a high decrease at infinity. 相似文献
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In this paper, we mainly study the Cauchy problem of the generalized Degasperis-Procesi equation. We establish the local well-posedness and give the precise blow-up scenario for the equation. Then we show that the equation has smooth solutions which blow up in finite time. 相似文献
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Jamel Benameur 《Journal of Mathematical Analysis and Applications》2010,371(2):719-727
In this paper we prove some properties of the maximal solution of Navier-Stokes equations. If the maximum time is finite, we establish that the growth of is at least of the order of (see Eq. (1.4)), also we give some new blow-up results. Specific properties and standard techniques are used. 相似文献
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We first establish the local well-posedness for the Cauchy problem of a two-component water waves system in nonhomogeneous Besov spaces using the Littlewood–Paley theory. Then, we derive three new blow-up results for strong solutions to the system. Finally, we present two persistence properties for strong solutions to the system. 相似文献
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Joachim Escher 《Journal of Functional Analysis》2006,241(2):457-485
In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions. 相似文献
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The 3D magneto-micropolar equations with damping are considered in this paper. We prove the existence and uniqueness of strong solution for 3D magneto-micropolar equations with damping for with any . 相似文献
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The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state. 相似文献
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This paper is to derive a new blow-up criterion for the 2D full compressible Navier–Stokes equations without heat conduction in terms of the density and the pressure . More precisely, it indicates that in a bounded domain the strong solution exists globally if the norm for some constant satisfying . The boundary condition is imposed as a Navier-slip boundary one and the initial vacuum is permitted. Our result extends previous one which is stated as . 相似文献
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Peng Feng 《Journal of Mathematical Analysis and Applications》2007,329(1):347-356
In this paper we establish the exact blow-up rate of the large solutions of a porous media logistic equation. We consider the carrying capacity function with a general decay rate at the boundary instead of the usual cases when it can be approximated by a distant function. Obtaining the accurate blow-up rate allows us to establish the uniqueness result. Our result covers all previous results on the ball domain and can be further adapted in a more general domain. 相似文献
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Juntang Ding Xuyan Gao Shengjia Li 《Journal of Mathematical Analysis and Applications》2008,343(1):159-169
In this paper, we study the following reaction diffusion model,
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Piero D'Ancona 《Journal of Functional Analysis》2011,260(8):2300-2365
In recent work, Grünrock and Pecher proved that the Dirac-Klein-Gordon system in 2d is globally well-posed in the charge class (data in L2 for the spinor and in a suitable Sobolev space for the scalar field). Here we obtain the analogous result for the full Maxwell-Dirac system in 2d. Making use of the null structure of the system, found in earlier joint work with Damiano Foschi, we first prove local well-posedness in the charge class. To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis. For this we rely on the fact that MD is charge subcritical in two space dimensions, and make use of the null structure of the Maxwell part. 相似文献
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Global well-posedness of the non-isentropic full compressible magnetohydrodynamic equations
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In this paper, we are concerned with Cauchy problem for the multi-dimensional (N ≥ 3) non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and uniqueness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms. 相似文献