ar X iv : 0 90 1 . 45 48 v 1 [ m at h . N A ] 2 8 Ja n 20 09 THE NAVIER - STOKES - VOIGHT MODEL FOR IMAGE INPAINTING

ar X iv : 0 90 1 . 45 48 v 2 [ m at h . N A ] 2 8 Ja n 20 09 THE NAVIER - STOKES - VOIGHT MODEL FOR IMAGE INPAINTING

In 2001, Bertalmio, et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is obtained by numerically approximating the steady state solution of the 2D NSE vorticity transport equation, and simultaneously solving the Poisson problem bet...

ar X iv : 0 90 6 . 51 40 v 1 [ m at h . A P ] 2 8 Ju n 20 09 WELL - POSEDNESS FOR FRACTIONAL NAVIER - STOKES EQUATIONS IN CRITICAL SPACES

In this paper, we prove the well-posedness for the fractional NavierStokes equations in critical spaces G −(2β−1) n (R ) and BMO−(2β−1)(Rn). Both of them are close to the largest critical space Ḃ −(2β−1) ∞,∞ (R ). In G −(2β−1) n (R ), we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in BMO−(2β−1)...

ar X iv : 0 90 1 . 38 34 v 1 [ m at h . N T ] 2 4 Ja n 20 09 On the Inverse Problem Relative to Dynamics of the w Function

In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.

ar X iv : 0 90 6 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus

ar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.