2D Navier-Stokes equation in Besov spaces of negative order [PDF]
Nonlinear Analysis TMA 70 no. 11 (2009), 3902-3916, 2006 The Navier--Stokes equation in the bidimensional torus is considered, with initial velocity and forcing term in suitable Besov spaces. Results of local existence and uniqueness are proven; under further restriction on the indexes defining the Besov speces involved, we prove global existence.
arxiv
Smoothness criteria for Navier-Stokes equations in terms of regularity along the steam lines [PDF]
arXiv, 2007 This article is devoted to a regularity criteria for solutions of the Navier-Stokes equations in terms of regularity along the stream lines. More precisely, we prove that a suitable weak solution for the Navier-Stokes equations is regular under some constraint on the second derivative of |u| along the stream lines.
arxiv
Global regular solutions for the Navier-stokes system with small initial data in $Φ(2)$: an elementary approach [PDF]
arXiv, 2007 We show existence and regularity result for the Navier Stokes system for small data in the space $\Phi(2)$, and we show relations with some classical results.
arxiv
Global solutions for two-phase Hele-Shaw bubble for a near-circular initial shape [PDF]
arXiv, 2008 Using a vortex sheet method we prove global existence of a near circular initial bubble in a Hele-Shaw cell with surface tension and generally finite nonzero viscosity ratio between fluids inside and outside the bubble. The circular shape is shown to be asymptotically stable for all sufficiently smooth small perturbation.
arxiv
Global Strong Solution to the Density-Dependent Incompressible Viscoelastic Fluids [PDF]
arXiv, 2009 The existence and uniqueness of the global strong solution with small initial data to the three-dimensional viscoelastic fluids is established.
arxiv
Non-unique stationary solutions of even active scalar equations [PDF]
arXivWe study a class of active scalar equations with even non-local operator in the drift term. Non-trivial stationary weak solutions in the space $C^{0-}$ are constructed using the iterative convex integration approach.
arxiv
Well-posedness and blowup of 1D electron magnetohydrodynamics [PDF]
arXivThe one-dimensional toy models proposed for the three-dimensional electron magnetohydrodynamics in our previous work share some similarities with the original dynamics under certain symmetry. We continue to study the well-posedness issue and explore the potential singularity formation scenario for these models.
arxiv
A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient
Open Mathematics, 2014 Bosia Stefano +2 more
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Boundary regularity of flows under perfect slip boundary conditions
Open Mathematics, 2013 Kaplický Petr, Tichý Jakub
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