Related papers: Wave maps on (1+2)-dimensional curved spacetimes

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…

We consider Wave Maps with smooth compactly supported initial data of small H^{{3/2}}-norm from R^{3+1} to the hyperbolic plane and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb…

The localization length for classical waves in two dimensional random media is calculated exactly, and is compared with the theoretical prediction from the previous analytic theory. Significant discrepancies are observed. It is also shown…

We present the iterative classical point symmetry analysis of a shallow water wave equation in $2+1$ dimensions and that of its corresponding nonisospectral, two component Lax pair. A few reductions arise and are identified with celebrate…

An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existence of special solutions known as `double waves' is…

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

In this paper, we give a unified treatment of the local well-posedness for the wave kinetic equation in almost critical weighted $L^r$ spaces with $2 \leq r \leq \infty.$ The proof builds on ideas from our earlier works \cite{AmLe24,…

We consider the $L^2$-boundedness of the solution itself of the Cauchy problem for wave equations with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space. To study these, we adopt a simple multiplier method by…

Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…

We establish the existence of weak global solutions of the half-wave maps equation with the target $S^2$ on $\mathbb{R}^{1+1}$ with large initial data in $\dot{H}^1 \cap \dot{H}^{\frac{1}{2}}(\mathbb{R})$. We first prove the global…

We prove uniqueness of solutions to the wave map equation in the natural class, namely $ (u, \partial_t u) \in C([0,T); \dot{H}^{d/2})\times C^1([0,T); \dot{H}^{d/2-1})$ in dimensions $d\geq 4$. This is achieved through estimating the…

The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the 1+2-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary,…

We study the long time behavior of the subcritical (subcubic) defocussing nonlinear wave equation on the three dimensional ball, for random data of low regularity. We prove that for a large set of radial initial data in $\cap_{s<1/2}…

In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $\mathbb{S}^3$ and $\mathbb{H}^3$. In…

Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description of singular profiles appearing in long time wave evolution…

The use of geometrical constraints opens many new perspectives in photonics and in fundamental studies of nonlinear waves. By implementing surface structures in vertical cavity surface emitting lasers as manifolds for curved space, we…

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…

We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…

We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$,…

We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…