TY - JOUR
T1 - The Wave Maps Equation and Brownian Paths
AU - Bringmann, Bjoern
AU - Lührmann, Jonas
AU - Staffilani, Gigliola
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/3
Y1 - 2024/3
N2 - We discuss the (1+1)-dimensional wave maps equation with values in a compact Riemannian manifold. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting combines analytic, geometric, and probabilistic methods.
AB - We discuss the (1+1)-dimensional wave maps equation with values in a compact Riemannian manifold. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting combines analytic, geometric, and probabilistic methods.
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U2 - 10.1007/s00220-023-04885-5
DO - 10.1007/s00220-023-04885-5
M3 - Article
AN - SCOPUS:85187275245
SN - 0010-3616
VL - 405
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
M1 - 60
ER -