Exponential decay for soft potentials near Maxwellian. Strain, R. M. & Guo, Y. *Arch. Ration. Mech. Anal.*, 187(2):287–339, 2008.

Pdf doi abstract bibtex

Pdf doi abstract bibtex

Consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches to zero at the rate of $e^{-λ t^{p}}$ for some $λ >0$ and $p∈ (0,1)$. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical Caflisch 1980 result to the case of very soft potential and Coulomb interactions.

@article{MR2366140, abstract = {Consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches to zero at the rate of $e^{-\lambda t^{p}}$ for some $\lambda >0$ and $p\in (0,1)$. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical Caflisch 1980 result to the case of very soft potential and Coulomb interactions.}, author = {Strain, Robert M. and Guo, Yan}, date-added = {2019-07-13 15:27:26 -0400}, date-modified = {2019-08-08 11:40:38 -0600}, doi = {10.1007/s00205-007-0067-3}, fjournal = {Archive for Rational Mechanics and Analysis}, issn = {0003-9527}, journal = {Arch. Ration. Mech. Anal.}, keywords = {Boltzmann equation, Landau equation, Kinetic Theory}, mrclass = {82B05 (35B45 35F25)}, mrnumber = {2366140}, mrreviewer = {Simone Calogero}, number = {2}, pages = {287--339}, read = {0}, title = {Exponential decay for soft potentials near {M}axwellian}, urlpdf = {https://www2.math.upenn.edu/~strain/preprints/2005SGed.pdf}, volume = {187}, year = {2008}, zblnumber = {1130.76069}, Bdsk-Url-1 = {https://doi.org/10.1007/s00205-007-0067-3}}

Downloads: 0

{"_id":"sjotDCtriTLEF2QFY","bibbaseid":"strain-guo-exponentialdecayforsoftpotentialsnearmaxwellian-2008","authorIDs":["2auPNbhry7ALE7QjX","3Ed5RWpqr7rBqMaHC","5cecbf3980df6ada01000012","5de9d3a15e5ac8de01000117","5dedaaf35c662cef01000141","5df2532063aac8df01000034","5df65c61df30fcdf0100018e","5df8def2877972de01000112","5e00f28f08c773de0100005b","5e019d0ab81d0dde0100003f","5e114d06b59632f201000003","5e1242eac196d3de01000128","5e1295d1551229df0100009f","5e191011a7672ede010000f6","5e1f19a33cc57cde010000ea","5e1f77a208195af301000005","5e200593453fb7df01000016","5e253434561b8fde0100002e","5e28ba016acacbdf0100009b","5e2e310c185844df0100000f","5e3062e34988d7de01000009","5e39275f7f8bf3f3010000f8","5e509cd14e0862e401000049","5e51b44632046bdf01000075","5e556e5ee11ab9df01000044","5e5fbcd26b32b0f20100001f","5e62f940377bb9de0100007a","5e67f5720e29d3de01000302","5e6abe50d15181f301000048","5vpFLK7gjpx6zgqnE","9apjwcu85zcHXFgat","9ikmvbE9ZcFpS2Mj8","ATsJnBoiuXB3jXoYk","BFh5jHrpXbkvDQJhc","BKNSSwfvKksnMDkKk","Bd57YrqZ5e8SvANxK","D48rbZSbW3iDkfK4v","EayLyRKn3k9jtbghs","Eiy7qKEwgMrZ5FPn9","EwGabmbTRJzZ4yH4r","FwCCcBcxPQ4RWBZLY","H73AsjNAQkvgnYiYD","JWp4c4HsDwFFvpdnq","LWkk7jiojNqfCAN6j","LvjhbbDP5JwNGDePb","TXjywbQy6mNdjXDiC","XfghT3nq5AZD5N4Ge","XocTRevgx6CRnCBy9","Z42Jotrjs9jSmerjL","cad2QN2oCd5XF9d2q","dbAiJdvZDu2xpmqts","gTDudiGPStFxJar8R","kERf7FQqpBxLNDZhc","qtada8FpZ25ps85An","xNdWhAhM9FX27zahM"],"author_short":["Strain, R. M.","Guo, Y."],"bibdata":{"bibtype":"article","type":"article","abstract":"Consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches to zero at the rate of $e^{-λ t^{p}}$ for some $λ >0$ and $p∈ (0,1)$. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical Caflisch 1980 result to the case of very soft potential and Coulomb interactions.","author":[{"propositions":[],"lastnames":["Strain"],"firstnames":["Robert","M."],"suffixes":[]},{"propositions":[],"lastnames":["Guo"],"firstnames":["Yan"],"suffixes":[]}],"date-added":"2019-07-13 15:27:26 -0400","date-modified":"2019-08-08 11:40:38 -0600","doi":"10.1007/s00205-007-0067-3","fjournal":"Archive for Rational Mechanics and Analysis","issn":"0003-9527","journal":"Arch. Ration. Mech. Anal.","keywords":"Boltzmann equation, Landau equation, Kinetic Theory","mrclass":"82B05 (35B45 35F25)","mrnumber":"2366140","mrreviewer":"Simone Calogero","number":"2","pages":"287–339","read":"0","title":"Exponential decay for soft potentials near Maxwellian","urlpdf":"https://www2.math.upenn.edu/~strain/preprints/2005SGed.pdf","volume":"187","year":"2008","zblnumber":"1130.76069","bdsk-url-1":"https://doi.org/10.1007/s00205-007-0067-3","bibtex":"@article{MR2366140,\n\tabstract = {Consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches to zero at the rate of $e^{-\\lambda t^{p}}$ for some $\\lambda >0$ and $p\\in (0,1)$. Our method is based on an unified energy estimate with appropriate exponential velocity\nweight. Our results extend the classical Caflisch 1980 result to the case of very soft potential and Coulomb interactions.},\n\tauthor = {Strain, Robert M. and Guo, Yan},\n\tdate-added = {2019-07-13 15:27:26 -0400},\n\tdate-modified = {2019-08-08 11:40:38 -0600},\n\tdoi = {10.1007/s00205-007-0067-3},\n\tfjournal = {Archive for Rational Mechanics and Analysis},\n\tissn = {0003-9527},\n\tjournal = {Arch. Ration. Mech. Anal.},\n\tkeywords = {Boltzmann equation, Landau equation, Kinetic Theory},\n\tmrclass = {82B05 (35B45 35F25)},\n\tmrnumber = {2366140},\n\tmrreviewer = {Simone Calogero},\n\tnumber = {2},\n\tpages = {287--339},\n\tread = {0},\n\ttitle = {Exponential decay for soft potentials near {M}axwellian},\n\turlpdf = {https://www2.math.upenn.edu/~strain/preprints/2005SGed.pdf},\n\tvolume = {187},\n\tyear = {2008},\n\tzblnumber = {1130.76069},\n\tBdsk-Url-1 = {https://doi.org/10.1007/s00205-007-0067-3}}\n\n","author_short":["Strain, R. M.","Guo, Y."],"key":"MR2366140","id":"MR2366140","bibbaseid":"strain-guo-exponentialdecayforsoftpotentialsnearmaxwellian-2008","role":"author","urls":{"Pdf":"https://www2.math.upenn.edu/~strain/preprints/2005SGed.pdf"},"keyword":["Boltzmann equation","Landau equation","Kinetic Theory"],"metadata":{"authorlinks":{"strain, r":"https://www2.math.upenn.edu/"}},"html":""},"bibtype":"article","biburl":"https://www2.math.upenn.edu/~strain/RMS3web.bib","creationDate":"2019-05-28T02:42:04.779Z","downloads":3,"keywords":["boltzmann equation","landau equation","kinetic theory"],"search_terms":["exponential","decay","soft","potentials","near","maxwellian","strain","guo"],"title":"Exponential decay for soft potentials near Maxwellian","year":2008,"dataSources":["msqqTKyQkGRsrbM9j","FMWnDrXyyMWt4bcNj"]}