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Existence and Regularity of Renormalized Solutions for Boltzmann Equation

Mahmoudian, Hamid Reza | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51068 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fotouhi, Morteza
  7. Abstract:
  8. In 1989 DiPerna and Lions proved the stability of Boltzmann’s evolution equation using their theory of renormalized solutions. Their result , for the first time, proved the existence of solutions without extra assumptions on the initial condition and on arbitrary time intervals. While the wellknown Grad’s cut-off assumption is present in the original theory, there have been successful generalizations to account for the singular case. Also the renormalization theory has shed light on limiting regimes of the Boltzmann equation. Here we discuss the new techniques that are essential for such generalizations
  9. Keywords:
  10. Kinetic Theory ; Stability ; Entropy ; Boltzman Equation ; Grad Cut-Off ; Existence and Regularity ; Lions Conjecture

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