Limit clusters in the inviscid Burgers turbulence with certain random initial velocities
We study the infinite time shock limits given certain Markovian initial velocities to the inviscid Burgers turbulence. Specifically, we consider the one-sided case where initial velocities are zero on the negative half-line and follow a time-homogeneous nice Markov process X on the positive half-lin...
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| Format: | Journal article |
| Language: | English |
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2002
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| _version_ | 1826275854934605824 |
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| author | Winkel, M |
| author_facet | Winkel, M |
| author_sort | Winkel, M |
| collection | OXFORD |
| description | We study the infinite time shock limits given certain Markovian initial velocities to the inviscid Burgers turbulence. Specifically, we consider the one-sided case where initial velocities are zero on the negative half-line and follow a time-homogeneous nice Markov process X on the positive half-line. Finite shock limits occur if the Markov process is transient tending to infinity. They form a Poisson point process if X is spectrally negative. We give an explicit description when X is furthermore spatially homogeneous (a Lévy process) or a self-similar process on (0, ∞). We also consider the two-sided case where we suppose an independent dual process in the negative spatial direction. Both spatial homogeneity and an exponential Lévy condition lead to stationary shock limits. |
| first_indexed | 2024-03-06T23:05:09Z |
| format | Journal article |
| id | oxford-uuid:63852eb9-aca8-4eb6-931a-200341693c9c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:05:09Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:63852eb9-aca8-4eb6-931a-200341693c9c2022-03-26T18:13:32ZLimit clusters in the inviscid Burgers turbulence with certain random initial velocitiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:63852eb9-aca8-4eb6-931a-200341693c9cEnglishSymplectic Elements at Oxford2002Winkel, MWe study the infinite time shock limits given certain Markovian initial velocities to the inviscid Burgers turbulence. Specifically, we consider the one-sided case where initial velocities are zero on the negative half-line and follow a time-homogeneous nice Markov process X on the positive half-line. Finite shock limits occur if the Markov process is transient tending to infinity. They form a Poisson point process if X is spectrally negative. We give an explicit description when X is furthermore spatially homogeneous (a Lévy process) or a self-similar process on (0, ∞). We also consider the two-sided case where we suppose an independent dual process in the negative spatial direction. Both spatial homogeneity and an exponential Lévy condition lead to stationary shock limits. |
| spellingShingle | Winkel, M Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title | Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title_full | Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title_fullStr | Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title_full_unstemmed | Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title_short | Limit clusters in the inviscid Burgers turbulence with certain random initial velocities |
| title_sort | limit clusters in the inviscid burgers turbulence with certain random initial velocities |
| work_keys_str_mv | AT winkelm limitclustersintheinviscidburgersturbulencewithcertainrandominitialvelocities |