In this paper we prove that the cubic wave equation is globally well posed and scattering for radial initial data satisfying ‖|x|2ǫu0‖Ḣ1/2+ǫ(R3)+‖u0‖Ḣ1/2+ǫ(R3)+‖|x| 2ǫu1‖Ḣ−1/2+ǫ(R3)+‖u1‖Ḣ−1/2+ǫ(R3) < ∞. (0.1) This space of functions is slightly smaller than the general critical space, Ḣ× Ḣ.

In this paper, we show the global well-posedness for periodic gKdV equations in the space H(T), s ≥ 1 2 for quartic case, and s > 5 9 for quintic case. These improve the previous results of Colliander et al in 2004. In particular, the result is sharp in the quartic case.

We derive a formula for the n-row Macdonald polynomials with the coefficients presented both combinatorically and in terms of very-well-poised hypergeometric series.

We introduce and analyze a stable procedure for the approximation of 〈f†, φ〉 where f† is the least residual norm solution of the minimal norm of the ill-posed equation Af = g, with compact operator A : X → Y between Hilbert spaces, and φ ∈ X has some smoothness assumption. Our method is based on a finite number of singular values of A and some finite rank operators. Our results are in a more ge...

This paper is concerned with the mathematical analysis of the time-domain Maxwell equations in a three-dimensional open cavity. An exact transparent boundary condition is developed to reformulate the open cavity scattering problem in an unbounded domain, equivalently, into an initial-boundary value problem in a bounded domain. The well-posedness and stability are studied for the reduced problem...

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate L∞, BV and L estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.

We prove global well-posedness for the defocusing cubic wave equation

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the ...

This paper deals with the problem of existence of Berge and Berge–Nash equilibria. Abalo and Kostreva have proved existence theorems of Berge and Berge–Nash equilibria for S-equi-well-posed and (S, σ)equi-well-posed games, namely, Theorems 3.2–3.3 [Abalo, K.Y., Kostreva, M.M., 1996. Fixed Points, Nash Games and their Organization. Topological Methods in Nonlinear Analysis 8, 205–215.]. In this ...