We announce a result on the existence of a unique local solution to a stochastic geometric wave equation on the one dimensional Minkowski space with values in an arbitrary compact Riemannian manifold. We consider a rough initial data in the sense that its regularity is lower than the energy critical.
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@article{CRMATH_2020__358_6_633_0,
author = {Brze\'zniak, Zdzis{\l}aw and Rana, Nimit},
title = {Low regularity solutions to the stochastic geometric wave equation driven by a fractional {Brownian} sheet},
journal = {Comptes Rendus. Math\'ematique},
pages = {633--639},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {6},
year = {2020},
doi = {10.5802/crmath.38},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.38/}
}
TY - JOUR AU - Brzeźniak, Zdzisław AU - Rana, Nimit TI - Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet JO - Comptes Rendus. Mathématique PY - 2020 SP - 633 EP - 639 VL - 358 IS - 6 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.38/ DO - 10.5802/crmath.38 LA - en ID - CRMATH_2020__358_6_633_0 ER -
%0 Journal Article %A Brzeźniak, Zdzisław %A Rana, Nimit %T Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet %J Comptes Rendus. Mathématique %D 2020 %P 633-639 %V 358 %N 6 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.38/ %R 10.5802/crmath.38 %G en %F CRMATH_2020__358_6_633_0
Brzeźniak, Zdzisław; Rana, Nimit. Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet. Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 633-639. doi : 10.5802/crmath.38. http://www.numdam.org/articles/10.5802/crmath.38/
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