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(Local existence).
Step 2. Local existence.
Local existence [15, 16].
Local existence of smooth solutions.
Theorem (Local existence and uniqueness).
Local existence can be proved as [13].
First, we show the local existence results.
Theorem 1.1 (Local existence and uniqueness).
Next, we state two local existence theorems.
We first state two local existence theorems.
We begin with the local existence of solutions to (1.1).
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