On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments
The Boltzmann–Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Bolt...
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| Published in: | Journal of statistical physics Vol. 163; no. 5; pp. 1108 - 1156 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01-06-2016
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| Abstract | The Boltzmann–Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann–Nordheim equation for bosons, in dimension
d
⩾
3
. We show existence and uniqueness locally in time for any initial data in
L
∞
(
1
+
v
s
)
with finite mass and energy, for a suitable
s
, as well as the instantaneous creation of moments of all order. |
|---|---|
| AbstractList | The Boltzmann–Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann–Nordheim equation for bosons, in dimension
d
⩾
3
. We show existence and uniqueness locally in time for any initial data in
L
∞
(
1
+
v
s
)
with finite mass and energy, for a suitable
s
, as well as the instantaneous creation of moments of all order. The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann-Nordheim equation for bosons, in dimension d 3. We show existence and uniqueness locally in time for any initial data in L ∞ (1 + |v| s) with finite mass and energy, for a suitable s, as well as the instantaneous creation of moments of all order. The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann-Nordheim equation for bosons, in dimension . We show existence and uniqueness locally in time for any initial data in with finite mass and energy, for a suitable s, as well as the instantaneous creation of moments of all order. |
| Audience | Academic |
| Author | Briant, Marc Einav, Amit |
| Author_xml | – sequence: 1 givenname: Marc surname: Briant fullname: Briant, Marc email: briant.maths@gmail.com organization: Division of Applied Mathematics, Brown University – sequence: 2 givenname: Amit surname: Einav fullname: Einav, Amit organization: Centre for Mathematical Sciences, University of Cambridge DPMMS |
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| CitedBy_id | crossref_primary_10_1007_s00220_021_04029_7 crossref_primary_10_1016_j_jcp_2023_112197 crossref_primary_10_1016_j_aim_2023_109234 crossref_primary_10_1016_j_jfa_2019_108315 crossref_primary_10_1016_j_jfa_2023_110197 crossref_primary_10_1007_s00205_021_01643_6 crossref_primary_10_1007_s40324_021_00281_y crossref_primary_10_1016_j_jmaa_2017_12_052 crossref_primary_10_1016_j_jde_2022_01_056 crossref_primary_10_1016_j_jfa_2022_109737 crossref_primary_10_1137_19M1270021 crossref_primary_10_1016_j_aim_2017_12_007 crossref_primary_10_3934_krm_2022025 crossref_primary_10_1007_s10955_019_02258_8 crossref_primary_10_5802_jep_113 crossref_primary_10_1016_j_jfa_2018_09_010 crossref_primary_10_1007_s10955_019_02466_2 crossref_primary_10_1007_s10955_023_03082_x crossref_primary_10_1016_j_jfa_2020_108570 |
| Cites_doi | 10.1007/978-1-4419-8524-8 10.1023/B:JOSS.0000041750.11320.9c 10.1007/BF02398270 10.1016/S0167-2789(01)00211-1 10.1007/s00205-009-0250-9 10.1007/s10909-006-9232-6 10.1103/PhysRevLett.74.3093 10.1103/PhysRevD.55.489 10.1007/s10955-014-1026-7 10.1007/s00220-014-2034-9 10.1098/rspa.1928.0126 10.1016/S0294-1449(99)80025-0 10.1007/s00222-014-0539-7 10.1016/S1874-5792(02)80004-0 10.1007/s10955-005-3767-9 10.1007/978-1-4612-1039-9 10.1016/j.physd.2010.01.018 10.1007/BF01011586 10.1023/A:1018628031233 10.1023/A:1004606525200 10.1007/BF00253392 10.1142/S0129055X14500019 10.1007/BF00253393 10.1007/978-3-642-45892-7_3 10.1007/3-540-07171-7_1 |
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| Keywords | Subcritical solutions Boltzmann–Nordheim equation Bose–Einstein condensation Kinetic model for bosons Local Cauchy problem Boltzmann-Nordheim equation Bose- Einstein condensattion Local Cauchy Problem |
| Language | English |
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| Snippet | The Boltzmann–Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution... The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution... |
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| SubjectTerms | Analysis of PDEs Mathematical and Computational Physics Mathematical Physics Mathematics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| Title | On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments |
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