The initial value problem for the compressible Navier-Stokes equations without heat conductivity

Global Existence and Large Time Behavior for the 2-D Compressible Navier-Stokes Equations without Heat Conductivity

“…The motivation of this paper is to refine the previous works of [3,5]. As mentioned above, to prove the global existence of the compressible Navier-Stokes equations, ref.…”

“…As mentioned above, to prove the global existence of the compressible Navier-Stokes equations, ref. [3] needs to use some complicated techniques based on the notions of the homogeneous Besov space and the hybrid Besov space to remove a condition in [5]. However, in this paper, we use a much simpler method to achieve this, to complete a prior estimate on entropy S which is important to prove the global existence of the compressible Navier-Stokes equations by some simple analysis.…”

“…(1) The L q decay estimates of (7) for 2 ≤ q ≤ 4 are optimal which coincide with the L q decay of the heat equation and are much slower than the decay rate in ℝ 3 : In [3,5], they obtain that kuðtÞk…”

“…Among them, for the case with a positive coefficient of heat conduction k > 0, Kazhikhov and Shelukhin studied the global existence in one dimension [1,2]. The global existence of multidimensional case was established in [3][4][5][6]; more results on global existence for different kinds of solutions can be found in [3][4][5][6][7][8][9][10]. For the study of the large time behavior, asymptotic behavior, and optimal decay rates of solutions, one can refer to [4,[11][12][13][14][15].…”

“…Later, ref. [3] removed this assumption by using some techniques with regard to the homogeneous Besov space and the hybrid Besov space.…”