| EPSRC Reference: |
GR/N63055/01 |
| Title: |
ASYMPTOTICAL PROPERTIES OF RANDOMLY FORCED NONLINEAR PDES |
| Principal Investigator: |
Kuksin, Professor S |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
S of Mathematical and Computer Sciences |
| Organisation: |
Heriot-Watt University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2000 |
Ends: |
30 September 2003 |
Value (£): |
134,264
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The research will deal with randomly forced nonlinear partical differential equations. This is an important class of nonlinear PDEs which contains, for example, Navier-Stokes equations, disturbed by a random force. The goal of the research will be to study asymptotic properties of solutions for these equations. It was proved by the applicant and his Research Associate in the previous EPSRC financed one-year research project that an equation as above interpreted as a dynamical system in a function space possesses a unique invariant measure and probability characteristics of solutions for the equation converge to those of the measure. Thus the measure describes time-asympototics of the solutions. In this research a unique invariant measure as above will be constructed for a larger class of randomly forced PDEs in order to be able to deal with bigger class of physically important problems. For these equations the limiting behaviour of the invariant measure as viscosity goes to zero will be investigated. This limit corresponds to the transition to turbulence in a physical media, described by the equations. Since mathematical theory of turbulence practically does not exist, any progress in this problem is very important.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.hw.ac.uk |