共查询到20条相似文献,搜索用时 9 毫秒
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Chongsheng Cao 《Journal of Differential Equations》2010,248(9):2263-2274
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction. 相似文献
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Dongho Chae 《Advances in Mathematics》2006,203(2):497-513
In this paper, we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity. We also prove that as diffusivity (viscosity) tends to zero, the solutions of the fully viscous equations converge strongly to those of zero diffusion (viscosity) equations. Our result for the zero diffusion system, in particular, solves the Problem no. 3 posed by Moffatt in [R.L. Ricca, (Ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 3-10]. 相似文献
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Jiahong Wu 《Journal of Differential Equations》2003,195(2):284-312
Solutions of the d-dimensional generalized MHD (GMHD) equations
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Heinz-Otto Kreiss 《Journal of Differential Equations》2004,203(2):216-231
In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first derive corresponding a priori estimates for certain parabolic systems. Because of the pressure term, the case of the Navier-Stokes equations is more difficult, however. 相似文献
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We study the Cauchy problem for the n-dimensional Navier-Stokes equations (n?3), and prove some regularity criteria involving the integrability of the pressure or the pressure gradient for weak solutions in the Morrey, Besov and multiplier spaces. 相似文献
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We prove that a smooth solution of the 3D Boussinesq system with zero viscosity in a bounded domain breaks down, if a certain norm of vorticity blows up at the same time. Here this norm is weaker than the bmo-norm. 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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In this article we consider the following generalized quasi-geostrophic equation
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Jae-Myoung KIM 《数学物理学报(B辑英文版)》2018,38(6):1759-1766
We investigate the local existence of smooth solutions of a 3D ideal magnetohydrodynamics (MHD) equations in a bounded domain and give a blow-up criteria to this equations with respect to vorticists. 相似文献
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Antonio Russo 《Journal of Differential Equations》2011,251(9):2387-2408
The Navier problem is to find a solution of the steady-state Navier-Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity. We prove that a solution exists in a bounded domain provided ‖a‖L2(∂Ω) is less than a computable positive constant and is unique if ‖a‖W1/2,2(∂Ω)+‖s‖L2(∂Ω) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ‖a‖L2(∂Ω)+‖a−u0⋅n‖L2(∂Ω) is small. 相似文献
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Ruxu Lian 《Journal of Differential Equations》2010,248(8):1926-1954
The dynamical behaviors of vacuum states for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficient are considered. It is first shown that a unique strong solution to the free boundary value problem exists globally in time, the free boundary expands outwards at an algebraic rate in time, and the density is strictly positive in any finite time but decays pointwise to zero time-asymptotically. Then, it is proved that there exists a unique global weak solution to the initial boundary value problem when the initial data contains discontinuously a piece of continuous vacuum and is regular away from the vacuum. The solution is piecewise regular and contains a piece of continuous vacuum before the time T∗>0, which is compressed at an algebraic rate and vanishes at the time T∗, meanwhile the weak solution becomes either a strong solution or a piecewise strong one and tends to the equilibrium state exponentially. 相似文献
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In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations in R3. We prove the global existence of the smooth solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H3-framework. Moreover, if additionally the initial data belong to Lp with , the optimal convergence rates of the solutions in Lq-norm with 2≤q≤6 and its spatial derivatives in L2-norm are obtained. 相似文献
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Hyeong-Ohk Bae 《Journal of Differential Equations》2018,264(7):4889-4900
The regularity of 2D Navier–Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver–Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates. 相似文献
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In this paper, we consider the 3D Boussinesq equations with the incompressibility condition. We obtain a regularity condition for the three-dimensional Boussinesq equations by means of the Littlewood-Paley theory and Bony’s paradifferential calculus. 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
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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