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Global regularity for the 2D Boussinesq equations with partial viscosity terms
  • D. Chae
  • Mathematics, Materials Science
  • 10 July 2006
Abstract 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) tendsExpand
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Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations
Abstract: We consider the quasi-geostrophic equation with the dissipation term, κ (-Δ)α θ, In the case , Constantin-Cordoba-Wu [6] proved the global existence of strong solution in H1 and H2 underExpand
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The Existence of Non-Topological Multivortex Solutions in the Relativistic Self-Dual Chern–Simons Theory
Abstract: We construct a general type of multivortex solutions of the self-duality equations (the Bogomol'nyi equations) of (2+1) dimensional relativistic Chern–Simons model with the non-topologicalExpand
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Well-posedness for Hall-magnetohydrodynamics
We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a LiouvilleExpand
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On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
Abstract In this paper, we establish an optimal blow-up criterion for classical solutions to the incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in-timeExpand
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On the Spectral Dynamics of the Deformation Tensor and New A Priori Estimates for the 3D Euler Equations
  • D. Chae
  • Mathematics, Physics
  • 21 March 2005
In this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3D incompressible Euler equations. Using the evolution equation of the L2 norm of spectra, we deduceExpand
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On the regularity of the axisymmetric solutions of the Navier-Stokes equations
Abstract. We obtain improved regularity criteria for the axisymmetric weak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrabilityExpand
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Generalized surface quasi-geostrophic equations with singular velocities
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The firstExpand
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