| Abstract: |
| In this talk, I show that the Cauchy problem for isothermal Euler equations with relaxation admits a unique global smooth solution when either the relaxation time or the initial datum is sufficiently small. The large smooth solution is then obtained when the relaxation time is sufficiently small. Moreover, I establish error estimates for the convergence of the large density of the Euler equations toward the solution of the heat equation as the relaxation time tends to zero. Besides classical energy estimates, a uniform estimate for a quantity related to Darcy`s law is important in the proof of the above results. |
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