a remark on regularity criterion for the dissipative quasi geostrophic equations abstract this paper concerns with a regularity criterion of solutions to the 2d dissipative quasi geostrophic equations based on a logarithmic sobolev inequality in besov spaces the absence of singularities of in 0 t is derived for a solution on the interval 0 t satisfying the condition l r 0 t b p 0 for 2 p r 4 p this is an extension of earlier regularity results in the serrin s type space l r 0 t l p

dissipative quasi geostrophic equation for large initial data in the critical sobolev space the critical and super critical dissipative quasi geostrophic equations are investigated in mathbb r 2 we prove local existence of a unique regular solution for arbitrary initial data in h2 2 which corresponds to the scaling invariant space of the equation we also consider the behavior of the solution near t 0 in the sobolev space

asymptotic convergence rate of supercritical surface quasi geostrophic equation in morrey space abstract in this paper the asymptotic convergence rate of the supercritical surface quasi geostrophic equation in morrey space is investigated it is shown that if the global solution x t of the supercritical surface quasi geostrophic equation satisfies the growth condition in critical morrey space 0 t m p q r 2 r d t for r 2 p 2 p then every perturbed weak solution x t of the perturbed quasi geostrophic equation converges asymptotically to x t with the optimal rate t t l 2 o 1 t 1 as t in particular the initial perturbation is allowed large the findings are based on the spectral decomposition methods of fractional laplace and morrey space technique

global well posedness for the critical 2d dissipative quasi geostrophic equation we give an elementary proof of the global well posedness for the critical 2d dissipative quasi geostrophic equation the argument is based on a non local maximum principle involving appropriate moduli of continuity

on the blow up criterion for the quasi geostrophic equations in homogeneous besov spaces abstract in this paper we consider the blow up criterion for the quasi geostrophic equations with dissipation 0 1 by establishing a new trilinear estimate we show that if l s 1 0 t b s r 2 for some s 1 2 1 then the solution can be extended smoothly past t this improves and extends the corresponding results in dong and pavlovic 2009 32 and yuan 2010

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

chromatic scheduling in a cyclic open shop abstract we consider the computational complexity of some problems of scheduling in a cyclic open shop which is a variation of a standard open shop system in particular we show that the problem of scheduling is np hard for a 3 processor system and polynomial for a 2 processor one moreover we prove that the problem of determining if a given shop can be scheduled in 3 time units is polynomially solvable we also consider another variation of a cyclic open shop a compact open shop for this system we prove that the problem of minimizing c max for 2 processor system and the problem of determining if there exists a legal schedule are np hard moreover we give polynomial time algorithms for determining if c max 3 in a general case and for determining if c max 4 in the case of zero unit time tasks

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

on regularity criterion for the dissipative quasi geostrophic equations abstract in this paper we consider the 2d dissipative quasi geostrophic equations and study the regularity criterion of the solutions by means of a commutator estimate based on frequency localization and bony s paraproduct decomposition we obtain a regularity criterion l r 0 t b p 0 for 2 p r 2 p which is an obvious extension of the result in b dong z chen a remark on regularity criterion for the dissipative quasi geostrophic equations j math anal appl 329 2007 1212 1217 where their restrictive condition on p is 4 p

np hardness of compact scheduling in simplified open and flow shops abstract in practical task scheduling it is sometimes required that the components of a system perform consecutively such a scheduling is called scheduling without waiting periods or no wait and or no idle in this article we study the complexity of some simplified scheduling problems of this kind in open shop and flow shop settings in particular we show that many trivial questions about the existence of schedule become np hard even if there are only two machines or if the scheduling graph of a system is a path or a cycle

commutator estimate and its application to regularity criteria of the dissipative quasi geostrophic equation abstract a new commutator estimate with respect to a nonlinear convection upper bounded by a single partial derivative component in hilbert spaces is obtained as an application regularity criteria on the supercritical quasi geostrophic equation are obtained provided that solution growth conditions are assumed to involve a single partial derivative component

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

a two dimensional model for quasigeostrophic flow comparison with the two dimensional euler flow abstract a simple two dimensional model for quasigeostrophic flow is contrasted with the two dimensional incompressible euler equations the model arises under the assumptions of fast rotation uniform stratification and uniform potential vorticity it is found that the more loca feed back of the quasigeostrophic model gives rise to strongly nonlinear front formation as opposed to two dimensional euler where the steepening process of mature fronts obeys a nonlocal nearly linear mechanism

existence and uniqueness of the solution to the dissipative 2d quasi geostrophic equations in the sobolev space we study the two dimensional dissipative quasi geostrophic equations in the sobolev space open image in new window existence and uniqueness of the solution local in time is proved in h s when s 2 1 existence and uniqueness of the solution global in time is also proved in h s when s 2 1 and the initial data open image in new window is small for the case s 2 1 we also obtain the unique large global solution in h s provided that open image in new window is small enough

a note on distributed estimation and sufficiency in relation to distributed parameter estimation the notion of local and global sufficient statistics is introduced it is shown that when a sufficiency condition is satisfied by the probability distribution of a random sample a global sufficient statistic is obtainable as a function of local sufficient statistics several standard distributions satisfy the said sufficiency condition

a logarithmically improved regularity criterion for the surface quasi geostrophic equation abstract in this paper we consider the two dimensional dissipative surface quasi geostrophic equation and establish a logarithmically improved regularity criterion consequently our result extends the regularity criterion result of dong and pavlovie 2009 in addition a logarithmically improved regularity criterion to the three dimensional navier stokes equations is also derived by the same arguments therefore this result extends and improves many previous works

l2 stability for solutions of subcritical quasi geostrophic equation with large perturbations abstract this paper concerns with the asymptotic stability for the weak solution of the two dimensional dissipative subcritical quasi geostrophic equation in the class l p 0 t l q r 2 for p 2 q 2 q 1 2 it is proved that although the initial data and external force perturbations from are large every perturbed weak solution converges asymptotically to in l 2 r 2 as t as a byproduct we also obtain the weak strong uniqueness criterion of subcritical quasi geostrophic equation which improves the earlier results

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

on the regularity criteria of a surface quasi geostrophic equation abstract we obtain regularity criteria for a quasi geostrophic equation that depends more on one direction than the others in particular we show that in the critical case the global regularity depends only on a partial derivative rather than a gradient of the solution

regularity criteria for the dissipative quasi geostrophic equations in holder spaces we study regularity criteria for weak solutions of the dissipative quasi geostrophic equation with dissipation 2 0 1 we show in this paper that if theta in c 0 t c 1 gamma or theta in l r 0 t c alpha with alpha 1 gamma frac gamma r is a weak solution of the 2d quasi geostrophic equation then is a classical solution in 0 t times mathbb r 2 this result improves our previous result in 18