On Inner Regularity of Solutions of Two-Dimensional Zakharov–Kuznetsov Equation

Stationary periodic solutions of the two-dimensional Gross-Pitaevskii equation

Stationary periodic solutions of the two-dimensional Gross-Pitaevskii equation are obtained and analyzed for different parameter values in the context of the problem of a supersonic flow of a Bose-Einstein condensate past an obstacle. The asymptotic connections with the corresponding periodic solutions of the Korteweg-de Vries and nonlinear Schrödinger equations are studied and typical spatial ...

effect of oral presentation on development of l2 learners grammar

this experimental study has been conducted to test the effect of oral presentation on the development of l2 learners grammar. but this oral presentation is not merely a deductive instruction of grammatical points, in this presentation two hypotheses of krashen (input and low filter hypotheses), stevicks viewpoints on grammar explanation and correction and widdowsons opinion on limited use of l1...

Partial Regularity of Brenier Solutions of the Monge-ampère Equation

Given Ω,Λ ⊂ R two bounded open sets, and f and g two probability densities concentrated on Ω and Λ respectively, we investigate the regularity of the optimal map ∇φ (the optimality referring to the Euclidean quadratic cost) sending f onto g. We show that if f and g are both bounded away from zero and infinity, we can find two open sets Ω′ ⊂ Ω and Λ′ ⊂ Λ such that f and g are concentrated on Ω′ ...

Sobolev Regularity of Solutions of the Cohomological Equation

Wellposedness and regularity of solutions of an aggregation equation

We consider an aggregation equation in Rd, d ≥ 2 with fractional dissipation: ut + ∇ · (u∇K ∗ u) = −νΛγu, where ν ≥ 0, 0 < γ ≤ 2 and K(x) = e−|x|. In the supercritical case, 0 < γ < 1, we obtain new local wellposedness results and smoothing properties of solutions. In the critical case, γ = 1, we prove the global wellposedness for initial data having a small Lx norm. In the subcritical case, γ ...