Related papers: Sharp global regularity for the 2+1-dimensional eq…

This article addresses the large data global regularity for the equivariant case of the $2+1$-dimensional Faddeev model and shows that it holds true for initial data in $H^s\times H^{s-1}(\mathbb{R}^2)$ with $s>3$.

The Faddeev model is a classical field theory that models heavy elementary particles by knotted topological solitons. It is a generalization of the well-known classical nonlinear sigma model of Gell-Mann and Levy, and is also related…

This paper is concerned with the Cauchy problem of the evolutionary Faddeev model, a system that maps from the Minkowski space $\mathbb{R}^{1+3}$ to the unit sphere $\mathbb{S}^2$. The model is a system of nonlinear wave equations whose…

In this paper, for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1+n}$ to the unit sphere $\mathbb{S}^2$, we show the global nonlinear stability of geodesic solutions, which are a kind of nontrivial…

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1 + n}$ to the unit sphere $\mathbb{S}^2$, which obey a system of non-linear wave equations. The nonlinearity enjoys…

In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove global well-posedness result for small initial data lying in critical Besov spaces constructed…

We prove that the half-wave maps problem on $\mathbb{R}^{4+1}$ with target $S^2$ is globally well-posed for smooth initial data which are small in the critical $l^1$ based Besov space. This is a formal analogue of the result for wave maps…

We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain…

This paper is concerned with the regularity of solutions to parabolic evolution equations. We consider semilinear problems on non-convex domains. Special attention is paid to the smoothness in the specific scale $B^r_{\tau,\tau}$,…

In this paper, we show almost global existence of small solutions to the Cauchy problem for symmetric system of wave equations with quadratic (in 3D) or cubic (in 2D) nonlinear terms and multiple propagation speeds. To measure the size of…

We formulate the half-wave maps problem with target $S^2$ and prove global regularity in sufficiently high spatial dimensions for a class of small critical data in Besov spaces.

This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale…

In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global well-posedness and scattering holds for small initial data in…

The first target of this article is the local well-posedness question for 1D quasilinear Schr\"odinger equations with cubic nonlinearities. The study of this class of problems, in all dimensions, was initiated in pioneering work of…

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…

We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported initial data with sufficiently small…

In this paper we prove global well-posedness and scattering for the conformal, defocusing, nonlinear wave equation with radial initial data in the critical Sobolev space, for dimensions $d \geq 4$. This result extends a previous result…

We classify the Lie point symmetries for the 2+1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible f(u) functional forms where the latter depends. For each case the one-dimensional optimal system is…

In this paper, we consider the modified quasi-geostrophic equation \begin{gather*} \del_t \theta + (u \cdot \grad) \theta + \kappa \Lambda^\alpha \theta = 0 u = \Lambda^{\alpha - 1} R^{\perp}\theta. \end{gather*} with $\kappa > 0$, $\alpha…

We consider the initial value problem for the 2D quasi-geostrophic equation with weak dissipation term $\kappa(-\Delta)^{\alpha/2}\theta\ (0<\alpha\leqslant 1)$ and dispersive forcing term $Au_2$. We establish a unique global solution for a…