Đề tài " Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing " pdf

... Define C n = ρ n+1  10 ρ n  10 , Annals of Mathematics, 164 (2006), 993–1032 Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing By Martin Hairer and Jonathan C. Mattingly Abstract The stochastic 2D Navier-Stokes ... under the nonlinearity of the 2D Navier-Stokes equations (i.e. they are preserved by the flow of (1.1)...

Ngày tải lên: 29/03/2014, 07:20

... and let F n be the union of F n−1 with the loop-erasure of X n . Then F :=  ∞ n=1 F n has the distribution of the (wired) USF on G. The edges in F inherit the orientation from the loop-erased walks ... further condition on the occurrence of S, then we should also contract the edges in K 1 and delete the edges in K 2 . Therefore, conditionally on Υ R and the oc...

Ngày tải lên: 14/02/2014, 17:20

... by adding a ver- tex v to the list η(t), then [η :˜η]is(−1) k+d−1 , where k is the position of v in ˜η(t), and d is the dimension of the product of the simplices with the ver- tex sets η(1), ,η(t ... ∈ ¯ S, let ←− s be the leftmost element of the first gap to the left of the gap containing s, and let −→ s be the leftmost element of the first gap to the ri...

Ngày tải lên: 06/03/2014, 08:21

... can approximate V with open subsets of ML g,n satisfying (6.3), the measure ν J belongs to the Lebesgue measure class. Then the ergodicity of the 122 MARYAM MIRZAKHANI action of the mapping class ... closed curves In this section we use the ergodicity of the action of the mapping class group on the space of measured laminations to obtain the following res...

Ngày tải lên: 06/03/2014, 08:21

... hence ∞ sup n=0 C n |a (n) | ∞ < ∞. Therefore the radius of convergence of each entry of ψ is infinite. 3.1.4. Remark. Theorem 3.1.1 is in essence the (dual) t-motivic translation of Yu’s Theorem of the t-Submodule ... σ]-module structure by the rule σe := e (−1) (e ∈E). Put H 0 := ¯ k[t]-span in E of the entries of the vector ψ, V := ¯ k-span in k ∞ of the ent...

Ngày tải lên: 22/03/2014, 16:20

... ,x n )dx i  . The first invariants are the adapted order r = ν(F,E; P), that is the minimum of the orders of the coefficients b i , and the adapted multiplicity m = µ(F,E; P) defined as the minimum of the ... most of them not present in the nondicritical situations. Moreover, the nonresonant dicriticalness (appearing in the study of good points) is responsible for...

Ngày tải lên: 28/03/2014, 22:20

... −t). Note that the radius r T of the ball B(x T ,r T ) where the first integral of the right-hand side of (2.38) is computed is proportional to √ T −t, which is the width of the parabolic cone with vertex ... ε|  and the proof is complete. 54 F. BETHUEL, G. ORLANDI, AND D. SMETS 2. Toolbox The purpose of this section is to present a number of tools, which will en...

Ngày tải lên: 29/03/2014, 07:20

... in the proof of (93). The remaining term on the left-hand side of (93) is easier to treat. 7. Proof of the L 2 − L ∞ decay estimate; Theorem 2.1 In this section we rely on the Boundedness Theorem ... EQUATIONS 1155 In the proof of Theorem 3.4 we need the following comparison between the quantity Q(t) and the auxiliary norm E(t)=E[ψ](t). Theorem 3.5 (The comparison...

Ngày tải lên: 16/02/2014, 05:20

... data: (i) the intervals (I k ) 0≤k≤N/n 1  , (ii) the restriction of C to the union of the I k s, (iii) the values of C outside the I k s. Let us count in each case the number of possibilities: (i) There ... )+ Λδ 4 ) . For the remaining intervals, of length strictly less than n 1 , there can be at most (1−τ)N of them; this gives l (1−τ)Nn 1 possibilities. (iii) F...

Ngày tải lên: 06/03/2014, 08:21

... estimate the small ball probability using Lemma 5.2 and the size of the ε-net using Lemma 8.1. Note that only the second estimate uses the profile of the vectors. Then we conclude the proof with the ... n. Remark 9.1. The proof shows that the set of vectors of a regular profile is critical. On the other sets the norm of Ax is much greater with probability e...

Ngày tải lên: 15/03/2014, 09:20