We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy, and in the unpinned case also conserves the momentum. We obtain a time-inhomogeneous OrnsteinUhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit...

In this paper, we study a hydrodynamical system modeling the deformation of vesicle membrane in incompressible viscous fluids. In three dimensional case, we establish some uniqueness criteria of weak solutions for this system which reveal that the regularity of velocity field alone controls the uniqueness of weak solutions. Mathematics subject classification (2010): 35A02, 35G31, 76D09, 76T10.

Abstract. The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere S. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert e...

We present some new regularity criteria for “suitable weak solutions” of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm L x,t with 3/p + 2/q ≤ 2, 2 < q ≤ ∞, (p, q) 6= (3/2,∞), is small near the boundary. Our methods yield new results in the interior case as well....

In his Introduction to Metamathematics [13, § 64], S.C. Kleene distinguishes between a “strong sense” and a “weak sense” of propositional connectives when partially defined predicates are present. Each of these meanings is made explicit via certain 3-valued truth tables, which have become widely known as strong Kleene tables and weak Kleene tables, respectively. If the elements of the base set ...

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.