# Small Data Wave Maps in Cyclic Spacetime

@article{Yagdjian2020SmallDW, title={Small Data Wave Maps in Cyclic Spacetime}, author={Karen Yagdjian and Anahit Galstian and Nathalie M. Luna-Rivera}, journal={Springer INdAM Series}, year={2020} }

We study the initial value problem for the wave maps defined on the cyclic spacetime with the target Riemannian manifold that is responsive (see definition of the self coherence structure) to the parametric resonance phenomena. In particular, for arbitrary small and smooth initial data we construct blowing up solutions of the wave map if the metric of the base manifold is periodic in time.

## References

SHOWING 1-10 OF 30 REFERENCES

### Parametric Resonance in Wave Maps

- Mathematics
- 2011

In this note we concern with the wave maps from the Lorentzian manifold with the periodic in time metric into the Riemannian manifold, which belongs to the one-parameter family of Riemannian…

### Global Wave Maps on Robertson–Walker Spacetimes

- Mathematics
- 2000

We prove the global existence and uniqueness of wave maps onexpanding universes of dimension three or four, that is Robertson–Walkerspacetimes whose inverse radius is integrable with respect to the…

### Global Existence of Small Equivariant Wave Maps on Rotationally Symmetric Manifolds

- Mathematics
- 2015

We introduce a class of rotationally invariant manifolds, which we call admissible, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant…

### A remark on parametric resonance for wave equations with a time periodic coefficient

- Mathematics
- 2011

The Cauchy problem for a wave equation with a time periodic coefficient is considered. We prove that if one of the initial data is a compactly supported smooth function and the other initial data is…

### Parametric Resonance and Nonexistence of the Global Solution to Nonlinear Wave Equations

- Mathematics
- 2001

We give an example of the influence of the dependence of the coefficient of equation on time variable, and in particular oscillations in time, on a global existence of the solution to the nonlinear…

### Concentration Compactness for Critical Wave Maps

- Mathematics
- 2012

Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are…

### Global Regularity of Wave Maps from R2+1 to H2. Small Energy

- Mathematics
- 2004

We demonstrate that Wave Maps with smooth initial data and small energy from R2+1 to the Lobatchevsky plane stay smooth globally in time. Our method is similar to the one employed in [18]. However,…

### Remark on the optimal regularity for equations of wave maps type

- Mathematics
- 1997

The goal of this paper is to review the estimates proved in [3] and extend them to all dimensions, in particular to the harder case of space dimension 2. As in [3], the main application we have in…

### Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation

- Mathematics
- 2005

We consider nonlinear wave equations with variable coefficients. Special attention is devoted to the parametric resonance phenomena.