共查询到20条相似文献,搜索用时 390 毫秒
1.
Roger Alexander 《Communications in Mathematical Physics》1976,49(3):217-232
We construct the time evolution for infinitely many particles in
F(x) = { *20c + ¥ 0 *20c |x| < a |x| \geqq a \Phi (x) = \left\{ {\begin{array}{*{20}c} { + \infty } \\ 0 \\ \end{array} } \right. \begin{array}{*{20}c} {|x|< a} \\ {|x| \geqq a} \\ \end{array} 相似文献
2.
In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we
prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces
\mathringB1-a¥,q{\mathring{B}^{1-\alpha}_{\infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in
\mathringB0¥,q{\mathring{B}^{0}_{\infty,q}} for all 1 ≤ q < ∞. Here
\mathringBs¥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of Bs¥,q{B^{s}_{\infty,q}}. 相似文献
3.
Tadahiro Oh 《Communications in Mathematical Physics》2009,292(1):217-236
We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space [^(b)]sp,¥{\widehat{b}^s_{p,\infty}} , sp < −1, contains the support of the white noise. Then, we prove local well-posedness in [^(b)]sp, ¥{\widehat{b}^s_{p, \infty}} for p = 2 + ,
s = -\frac12+{s = -\frac{1}{2}+} such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical
proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21]. 相似文献
4.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
5.
For a q × q matrix x = (x i, j ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x
i, j
) we let J(x)=(xi,j-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(xi,j)-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kn=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=limn?¥( deg(Kn) )1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet. 相似文献
6.
Nakao Hayashi Pavel I. Naumkin Jean-Claude Saut 《Communications in Mathematical Physics》1999,201(3):577-590
We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP where = 1 or = m 1. When = 2 and = m 1, (KP) is known as the KPI equation, while = 2, = + 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case = 3, = m 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if S 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: ||u(t)||¥ £ C (1 + |t|)-1 (log(2+|t|))k, ||ux(t)||¥ £ C (1 + |t|)-1 \|u(t)\|_\infty \le C (1 + |t|)^{-1} (\log (2+|t|))^{\kappa}, \|u_x(t)\|_\infty \le C (1 + |t|)^{-1} for all t ] R, where s = 1 if = 3 and s = 0 if S 4. We also find the large time asymptotics for the solution. 相似文献
7.
Manoussos G. Grillakis Matei Machedon Dionisios Margetis 《Communications in Mathematical Physics》2010,294(1):273-301
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential ${v(x)= \epsilon \chi(x) |x|^{-1}}Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schr?dinger equation that describes
a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle
system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay
properties, implies a new Fock space estimate. We also show that for an interaction potential v(x) = ec(x) |x|-1{v(x)= \epsilon \chi(x) |x|^{-1}}, where e{\epsilon} is sufficiently small and c ? C0¥{\chi \in C_0^{\infty}} even, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and
sophisticated estimates for a subsequent part (Part II) of this paper. 相似文献
8.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
9.
C?t?lin I. Carstea 《Communications in Mathematical Physics》2010,300(2):487-528
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}
10.
We analyze the long time behavior of solutions of the Schrödinger equation ${i\psi_t=(-\Delta-b/r+V(t,x))\psi}
11.
Louis-Pierre Arguin Michael Damron C. M. Newman D. L. Stein 《Communications in Mathematical Physics》2010,300(3):641-657
We consider the Edwards-Anderson Ising spin glass model on the half-plane
\mathbbZ ×\mathbbZ+{\mathbb{Z} \times \mathbb{Z}^+} with zero external field and a wide range of choices, including mean zero Gaussian for the common distribution of the collection
J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution K(J,a){\mathcal{K}(J,\alpha)} of couplings J and ground state pairs α with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to
exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution K(a | J){\mathcal{K}(\alpha\,|\,J)} is supported on a single ground state pair. 相似文献
12.
For weakly non ergodic systems, the probability density function of a time average observable
is
where
is the value of the observable when the system is in state j=1,…L. p
j
eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed
balance conditions, p
j
eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x
2〉∼t
α
found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered
. We briefly discuss possible physical applications in single particle experiments. 相似文献
13.
Siegfried Bethke 《The European Physical Journal C - Particles and Fields》2009,64(4):689-703
Measurements of α
s, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world
average of as(MZ0)\alpha_{\mathrm{s}}(M_{\mathrm{Z}^{0}}) is derived. Special emphasis is laid on the most recent determinations of α
s. These are obtained from τ-decays, from global fits of electroweak precision data and from measurements of the proton structure function F2, which are based on perturbative QCD calculations up to O(as4)\mathcal{O}(\alpha_{\mathrm{s}}^{4}); from hadronic event shapes and jet production in e+e− annihilation, based on O(as3)\mathcal{O}(\alpha_{\mathrm{s}}^{3}) QCD; from jet production in deep inelastic scattering and from ϒ decays, based on O(as2)\mathcal{O}(\alpha_{\mathrm{s}}^{2}) QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. A pragmatic method is chosen to obtain the world
average and an estimate of its overall uncertainty, resulting in
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