Mathematical Sciences: Analysis of Collisionless Plasmas
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
The purpose of this research will be to analyze models of the              time evolution of collisionless plasmas moving under the influence              of their self-induced electromagnetic fields.  These models take                the form of systems of partial differential equations, the Poisson-             Vlasov system and the Maxwell-Vlasov system.  The unknown in each               model is the density of the plasma, and the Maxwell-Vlasov system               is somewhat more complete of the two systems, exhibiting electrical             and magnetic effects as well as relativistic.                                        Globally symmetric solutions were first established in 1952,               and numerous extensions followed.  However, the problem of global               existence of classical solutions for general data is still open                 for either system.  Recent results establish the breakdown of                   certain solutions in finite time.  One goal of this work will be                to show that when the initial data is nearly spherically                        symmetric, global existence of solutions is guaranteed.  A second               line of investigation proposes to model the interaction between                 the solar wind and the earth's magnetic field.  By this one                     understands the neutral stream of charged particles moving rapidly              away from the sun.  It consists mainly of protons and electrons                 which, when they encounter the earth's magnetic field, induce                   currents adding to the total magnetic field.  The resulting                     interaction is believed to account for the aurora borealis and                  geomagnetic storms.  Another feature of this interaction is a bow               shock wave across which the behavior of the plasma changes                      abruptly.  The precise nature of shock waves in collisionless                   plasmas is still unclear.  A mixed initial value-boundary value                 problem is proposed to model the above interaction.  Initial work               to be done will be in establishing global existence results for                 solutions and to determine conditions under which solutions tend to             a steady state as time increases.                                                    Applications to the physical sciences are clear.
{'FirstName': 'Jack', 'LastName': 'Schaeffer', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jack Schaeffer', 'EmailAddress': 'js5m@andrew.cmu.edu', 'NSF_ID': '000281780', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Carnegie-Mellon University', 'CityName': 'PITTSBURGH', 'ZipCode': '152133815', 'PhoneNumber': '4122688746', 'StreetAddress': '5000 FORBES AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA', 'CONGRESSDISTRICT': '18', 'CONGRESS_DISTRICT_ORG': 'PA18', 'ORG_UEI_NUM': 'U3NKNFLNQ613', 'ORG_LGL_BUS_NAME': 'CARNEGIE MELLON UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'U3NKNFLNQ613'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8801738.xml'}