{"abstracts":[{"sha1":"f6fcafd2dd4f48e3dd822996e6934607f4e522f1","content":"We study the stochastic viscous nonlinear wave equations (SvNLW) on 𝕋^2, forced by a fractional derivative of the space-time white noise ξ. In\nparticular, we consider SvNLW with the singular additive forcing\nD^1/2ξ such that solutions are expected to be merely distributions.\nBy introducing an appropriate renormalization, we prove local well-posedness of\nSvNLW. By establishing an energy bound via a Yudovich-type argument, we also\nprove global well-posedness of the defocusing cubic SvNLW. Lastly, in the\ndefocusing case, we prove almost sure global well-posedness of SvNLW with\nrespect to certain Gaussian random initial data.","mimetype":"text/plain","lang":"en"},{"sha1":"1cf96898abfdd873a08c8762def9869d29a6ea87","content":"We study the stochastic viscous nonlinear wave equations (SvNLW) on $\\mathbb\nT^2$, forced by a fractional derivative of the space-time white noise $\\xi$. In\nparticular, we consider SvNLW with the singular additive forcing\n$D^\\frac{1}{2}\\xi$ such that solutions are expected to be merely distributions.\nBy introducing an appropriate renormalization, we prove local well-posedness of\nSvNLW. By establishing an energy bound via a Yudovich-type argument, we also\nprove global well-posedness of the defocusing cubic SvNLW. Lastly, in the\ndefocusing case, we prove almost sure global well-posedness of SvNLW with\nrespect to certain Gaussian random initial data.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Ruoyuan Liu","role":"author"},{"index":1,"raw_name":"Tadahiro Oh","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v2","ext_ids":{"arxiv":"2106.11806v2"},"release_year":2021,"release_date":"2021-08-15","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["3elmgac2zndbzao337ouf7cyoy"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/2106.11806v2.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20210826084241/https://arxiv.org/pdf/2106.11806v2.pdf","rel":"webarchive"}],"sha256":"ba55f7253555ec5907e46430b76f6144f5e7c81cf67899c7cabc78103280fbe3","sha1":"420faa96c600676152b9f247c9a118cc9e855cf6","md5":"1134357bda0571c8ddd21641f4535120","size":314432,"revision":"7ccf32c6-bfcc-4b80-bf3e-669a2f10c3c6","ident":"wgft6n3bozb65jce4ktnji7iqu","state":"active"}],"work_id":"wf7trzjetzhsrcxtlchfbolfb4","title":"On the two-dimensional singular stochastic viscous nonlinear wave equations","state":"active","ident":"3elmgac2zndbzao337ouf7cyoy","revision":"e849d192-f253-4a10-92f6-c07e7417df74","extra":{"arxiv":{"base_id":"2106.11806","categories":["math.AP","math.PR"],"comments":"20 pages. Updated references"}}}